Educational Centre

Maths and physics behind simulations — from SPH hydrodynamics to Lorenz chaos and GLSL shaders. Read, learn, build.

50+Articles
15Tutorials
8References

💧 Particle Physics

27 articles
ArticlePhysics
SPH — Smoothed-Particle Hydrodynamics
Poly6, Spiky, Viscosity kernels. Pressure, viscosity, boundary conditions. Browser implementation.
ArticleAstrophysics
N-Body and the Barnes-Hut Algorithm
Leapfrog integrator, O(N²) vs O(N log N). Octree for scaling to 100k bodies.
ArticleMathematics
Verlet, Leapfrog and RK4 — Numerical Integration
Comparison of ODE integration methods: stability, accuracy, computational cost.
ArticlePhysics Simulation
XPBD: Extended Position-Based Dynamics Explained
XPBD (Extended Position-Based Dynamics) explained: compliant constraints, Lagrange multipliers, substepping, and why it fixed PBD's…
ArticleFluid Simulation
SPH with Free Surface — Simulating Splashes, Droplets & Waves
How Smoothed Particle Hydrodynamics handles free surfaces: kernel truncation, surface detection, continuum surface force tension, tensile instability, and…
ArticleFluid Simulation
FLIP Fluid: Particles + Grid
How the FLIP/PIC hybrid method combines Lagrangian particles with an Eulerian pressure grid to simulate incompressible fluid. P2G/G2P transfer, pressure…
ArticleAerodynamics
How Airplanes Fly — Two Theories and One Truth
The equal-transit fallacy explained. Learn the real aerodynamic physics of lift: pressure difference, circulation, and the Kutta-Joukowski theorem.
ArticleSports Physics
Cycling Aerodynamics — CdA, Drafting, and the Physics of Speed
The physics of cycling aerodynamics: CdA measurement, drag power, drafting benefit, altitude effects, position, and time-trial optimization.
ArticleGranular Physics
Discrete Element Method (DEM): Simulating Granular Materials
How DEM simulates sand, grains, rocks, and powders — contact force models, spring-dashpot mechanics, angle of repose, and force chains.
ArticleSports Physics
Bicycle Aerodynamics: The Science of Going Faster
The physics of cycling speed: drag coefficient, CdA, drafting, boundary layer, and rolling resistance.
ArticleFluid Dynamics
Navier-Stokes Equations — The Mathematics of Fluid Flow
Explore the Navier-Stokes equations, Reynolds number, laminar vs turbulent flow, the Kolmogorov cascade, and the Millennium Prize Problem.
ArticleFluid Simulation
Fluid Simulation Methods — SPH vs LBM vs MPM vs FEM
Compare fluid simulation approaches: SPH particles, Lattice Boltzmann, MPM, and grid-based FVM — performance, accuracy, and best use cases.
ArticleAerodynamics
How Aircraft Wings Generate Lift: Beyond Bernoulli
How wings generate lift explained — Kutta-Joukowski theorem, circulation, boundary layer, angle of attack, stall, and why Bernoulli alone is incomplete.
ArticleProjectile Physics
Ballistics and Aerodynamic Drag
The physics of projectile motion under aerodynamic drag: drag coefficients, terminal velocity, trajectory simulation, and ballistic coefficients.
ArticleFluid Dynamics
Boundary Layer and Drag — Prandtl's Theory of Viscous Flow
How Prandtl's boundary layer theory explains skin friction, the laminar-turbulent transition, the Blasius solution, and the drag crisis on a sphere.
ArticleFluid Physics
Capillary Action: How Plants Defy Gravity
How surface tension and capillary action let plants lift water against gravity, via the Young-Laplace equation and contact angles.
ArticleFluid Dynamics
Kármán Vortex Street: Flow Instability, Strouhal Number & LBM Simulation
The Kármán vortex street: Reynolds number regimes, Strouhal frequency scaling, linear stability theory, and a real-time Lattice-Boltzmann vortex-shedding simulation.
ArticleFluid Dynamics
Shallow Water Equations: Wave Propagation and Roe Solver
The shallow water equations govern long-wave dynamics in oceans, rivers, and atmospheres — conservation form, Roe solver, and a dam-break simulation.
ArticleFluid Physics
Why Are Soap Bubbles Round? Surface Tension Explained
Soap bubbles are always round because of surface tension. Learn about minimum surface area, the Laplace pressure equation, and why spheres are special.
ArticleFluid Dynamics
Magnus Effect — Spin, Lift and Curved Ball Flight
Magnus effect: how backspin and topspin generate aerodynamic lift via circulation, the Kutta-Joukowski theorem, and why tennis balls curve.
ArticlePhysics Simulation
Material Point Method (MPM) — Snow, Sand, and Fluid Simulation
How MPM works: Lagrangian particles plus Eulerian grid, P2G and G2P transfers, constitutive models for snow, sand and fluid, used in Disney's Frozen.
ArticleThermodynamics
Maxwell–Boltzmann Distribution — Kinetic Theory of Gases
Derive the Maxwell–Boltzmann speed distribution from first principles: Gaussian velocity components and characteristic speeds.
ArticlePlasma Physics
Magnetohydrodynamics: When Fluid Meets Magnetic Field
MHD explained — frozen-in theorem, Alfvén waves, magnetic pressure, reconnection, dynamo theory, and solar eruptions.
ArticleFluid Dynamics
Turbulence Explained — From Reynolds to Kolmogorov
How turbulence works: laminar-to-turbulent transition via Reynolds number, the Kolmogorov energy cascade, DNS vs LES vs RANS models, and the Kármán vortex street.
ArticleFluid Dynamics
Vortex Ring Dynamics — From Smoke Rings to Atomic Physics
Explore vortex ring dynamics: Helmholtz vortex theorems, the Biot-Savart law, self-propulsion, leapfrogging rings, and quantum vortices in Bose-Einstein condensates.
ArticleAerodynamics
NACA Airfoil & Wing Aerodynamics
NACA airfoil geometry, lift generation via Kutta-Joukowski, thin-airfoil theory, boundary layer separation, drag polar, and finite wing effects.
ArticleGranular Physics
Sand and Granular Materials — Angle of Repose & Falling Sand
Granular materials physics: angle of repose, force chains, cellular automata sand algorithm, Bagnold scaling, avalanches and self-organised criticality.

🌊 Waves & Fluids

24 articles
ArticleGLSL
Gerstner Waves in GLSL
Trochoidal waves, Fresnel effect, foam. Maths and vertex shader code.
ArticleMathematics
Wave Equation in 2D and 3D
Partial differential equations, finite differences, standing waves.
ArticlePhysics
Lattice Boltzmann Method (LBM)
CFD via statistics. D2Q9 model, BGK collision equation, turbulence in the browser.
ArticlePhysics
Navier-Stokes Equations in WebGL
Advection–diffusion–projection (Jos Stam "Stable Fluids"), projected-gradient solver.
ArticleFluid Dynamics
Turbulence & Reynolds Number
Turbulence and the Reynolds number: laminar-to-turbulent transition, Kolmogorov energy cascade, Kármán vortex street, DNS vs RANS vs LES modelling…
ArticleFluid Dynamics
Compressible and Expansion Flows: Shocks, Fans and Mach Number
Compressible and expansion flows explained — Mach number, isentropic relations, normal and oblique shock waves, Prandtl-Meyer expansion fans, and the…
ArticleFluid Dynamics
Shallow Water Equations: How Tsunamis Cross an Ocean
How the shallow water equations model tsunamis: depth-averaged mass and momentum conservation, wave speed √(gh), shoaling and run-up, dispersion, and…
ArticleBiomechanics
Swimming Hydrodynamics — Drag, Propulsion, and the Physics of the Stroke
The physics of swimming hydrodynamics: drag types, the propulsive vortex model, stroke mechanics, wave drag at the surface, buoyancy, wetsuit and swimsuit…
ArticleWave Physics
The Doppler Effect — From Sirens to Cosmology
How the Doppler effect shifts sound and light frequencies: sirens, radar guns, bat echolocation, and the expanding universe.
ArticleOptics & Photonics
How Lasers Work: Stimulated Emission & Population Inversion
How lasers amplify light through stimulated emission, population inversion, and optical cavities, from Einstein's 1917 prediction to today.
ArticleOptics & Photonics
Crystal Optics and Birefringence: When Light Splits in Two
Birefringent crystals like calcite split a light ray into two beams. Discover ordinary and extraordinary rays, optical axes, and interference colours between polarisers.
ArticleOptics
Caustics and Wave Focusing
Light caustics and wave focusing via refraction and reflection: Snell's law, focal points, underwater light patterns, and WebGL ray accumulation.
ArticleOptics
Rainbow Physics — Dispersion, Internal Reflection and Supernumerary Arcs
Why rainbows are round, why red is on top, and what causes supernumerary arcs and Alexander's dark band — the full optics of rainbows.
ArticleAtmospheric Optics
Rayleigh Scattering: Why the Sky Is Blue & Sunsets Are Red
The physics of light interacting with small particles, why the sky is blue, sunsets are red, and the maths behind Tyndall scattering and Mie theory.
ArticleElectromagnetism
Maxwell's Equations & Light — Electromagnetic Waves from First Principles
Derive electromagnetic waves from Maxwell's four equations: plane waves, polarisation, dispersion and Fresnel coefficients.
ArticleWave Optics
Diffraction & Interference — Wave Optics
Wave optics: Huygens-Fresnel principle, single-slit diffraction, double-slit interference, diffraction gratings, and the Airy disk limit.
ArticleGeophysics
Tsunami Physics: From Seafloor to Shore
Tsunami physics explained: generation, shallow-water wave equations, speed formula, wave shoaling, run-up, inundation modelling, and early warning systems.
ArticleOptics
How Holography Works: Recording Light as Wavefronts
A hologram records the light waves themselves, not an image. Discover how interference patterns encode full 3D information and coherent laser light reconstructs it.
ArticleElectromagnetism
Electric Field Potential and the Relaxation Method
Solving Laplace's equation on a 2D grid with Jacobi and Gauss-Seidel iterative solvers, visualising field lines and equipotentials via WebGL.
ArticleElectromagnetism
Electromagnetic Shielding — Faraday Cages and Skin Depth Physics
Explore the physics of electromagnetic shielding: Faraday cages, skin depth, shielding effectiveness, aperture effects, MRI rooms, and TEMPEST standards.
ArticleElectromagnetism
Faraday Induction & Plasma — Lenz's Law, MHD and the Pinch Effect
Faraday's law, Lenz's law, mutual induction, transformer equations, and magnetohydrodynamics — the physics of plasmas and the magnetic pinch effect.
ArticlePhysics
Coulomb's Law & Electric Fields — From Point Charges to Barnes–Hut
Coulomb's law, electric potential, Gauss's law for field lines, superposition of many charges, and the Barnes–Hut tree algorithm for N-body electrostatics.
ArticleOptical Physics
Optical Tweezers — Trapping Particles With Light
Optical tweezers trap microscopic particles using focused laser light — the physics of gradient forces and trapping regimes.
ArticleOptical Physics
Optical Tweezers: Trapping Particles with Light
A tightly focused laser beam traps microscopic particles — from glass beads to living cells — using nothing but light pressure.

🐦 Agent Algorithms

17 articles
ArticleSwarm Intelligence
Boids Algorithm — Reynolds' Three Rules
Separation, alignment, cohesion. Pseudocode, spatial partitioning, InstancedMesh.
ArticleAlgorithms
ACO — Ant Colony Optimisation
Pheromone trails, stigmergy, shortest-path finding. Canvas 2D implementation.
ArticleModelling
SIR/SEIR Epidemic Spread Model
Differential equations of population biology. R₀, herd immunity threshold.
ArticleMathematics
L-Systems and Plant Growth
Lindenmayer grammars, Turtle graphics, recursive trees, Barnsley fern.
ArticleGame AI
Behavior Trees for NPC AI
How behavior trees model complex NPC AI with Selectors, Sequences, Decorators, and a Blackboard. Compare with finite state machines and implement a JS BT…
ArticleMachine Learning
Reinforcement Learning: Intro to Q-Learning
How agents learn from reward alone: the Q-learning algorithm, the Bellman equation, exploration vs exploitation, and why it converges to the optimal…
ArticleEcology
Ecological Niches and Competition — Coexistence, Exclusion & the Lotka–Volterra Model
Ecological niches explained: Hutchinson's n-dimensional hypervolume, the competitive exclusion principle, Lotka–Volterra competition equations, niche…
ArticleBiophysics
Oxygen Diffusion in Tissue — Krogh's Cylinder Model
How oxygen travels from capillary blood into living tissue: Fick's law, the Krogh cylinder model, haemoglobin dissociation, and why the diffusion distance…
ArticleMathematical Biology
Tumor Growth: Avascular and Vascular
The mathematics and biology of tumor growth — Gompertz and logistic laws, diffusion-limited avascular spheroids, angiogenesis, and the switch to vascular…
ArticleBiomechanics
The Physics of Sprinting: Force, Power & Ground Contact
The biomechanics and physics of sprinting: horizontal force production, the force-velocity curve, ground contact time, drag, reaction time, and how elite…
ArticleSwarm Intelligence
How Do Ants Find Food? — Pheromones & Ant Colony Optimization
Ants leave chemical trails to share food directions. This simple trick is so powerful that computer scientists copied it for routing the internet.
ArticleSwarm Algorithms
Bee Algorithm and Artificial Bee Colony — Swarm Optimization from Waggle Dance
How honeybee foraging inspired the Artificial Bee Colony algorithm: scout bees, waggle dance encoding, and onlooker recruitment.
ArticleAnimal Behavior
How Do Bees Navigate? — The Waggle Dance Explained
A bee performs a figure-of-eight dance to tell hivemates exactly where flowers are — arguably the only non-human symbolic language on Earth.
ArticleSwarm Behavior
How Do Birds Fly in Flocks? — Boids, Murmuration & Emergence
Thousands of starlings seem to think together — but each bird follows just three simple rules. Discover the Boids algorithm and emergence.
ArticleSwarm Algorithms
Ant Colony Optimisation: How Ants Solve Hard Problems
Ant colony optimisation explained — stigmergy, pheromone trails, the TSP benchmark, ACO variants, and applications in routing and robotics.
ArticleEvolutionary Computation
NEAT: Neuroevolution of Augmenting Topologies — Evolving Neural Networks
The NEAT algorithm: how genetic encoding, speciation, structural innovations, and historical markings evolve both weights and topology of neural networks.
ArticleOptimization Algorithms
Particle Swarm Optimization (PSO) — Swarm Intelligence
A complete guide to PSO: the velocity update equation, inertia weight, cognitive and social components, and convergence analysis.

🌀 Chaos & Dynamic Systems

23 articles
ArticleChaos
Lorenz Attractor and the Butterfly Effect
Lorenz 1963 ODE system, sensitivity to initial conditions, strange attractor in 3D.
ArticleChaos
Double Pendulum and Runge-Kutta Method
Lagrange equations, RK4 numerical integration, Lyapunov chaos exponent.
ArticleFractal Geometry
IFS: Iterated Function Systems and Fractal Attractors
How Iterated Function Systems generate fractal attractors — the Barnsley fern, Sierpinski triangle — via the chaos game and the collage theorem.
ArticleChemical Dynamics
Belousov-Zhabotinsky Reaction: Chemistry's Oscillating Heart
The chemistry of oscillating reactions: the Oregonator model, spiral waves, Turing instability, and links to biological rhythms.
ArticleDynamical Systems
Bifurcation Diagrams: Period-Doubling, Feigenbaum & the Route to Chaos
Bifurcation diagrams of the logistic map: period-doubling cascade, the Feigenbaum constant, and the Lyapunov exponent.
ArticleStatistical Physics
Elastic Collisions & the Kinetic Theory of Gases
Elastic collisions are the foundation of the kinetic theory of gases, explaining how momentum and energy conservation give rise to temperature and pressure.
ArticleStatistical Physics
What Is Entropy? — Finally Understood
Entropy explained clearly: disorder, probability, Boltzmann's formula S = k ln W, thermodynamic entropy, and why reversible processes are impossible.
ArticleClassical Mechanics
How Does a Pendulum Work? — Simple Harmonic Motion Explained
Why does a pendulum keep perfect time? From Galileo's isochronism to the double pendulum's chaos — everything about pendulum physics.
ArticleStatistical Physics
Brownian Motion & Langevin Equation
Brownian motion from random walks to the Langevin SDE: diffusion coefficients, mean-squared displacement, and Wiener processes.
ArticleNonlinear Dynamics
Kuramoto Oscillators — The Math Behind Synchronized Fireflies and Heartbeats
The Kuramoto model of coupled oscillators: derivation, order parameter, critical coupling constant, and biological synchronization from fireflies to heartbeats.
ArticleChaos Theory
The Lorenz Attractor — How a Butterfly Changes the Weather
Explore the Lorenz attractor, sensitive dependence on initial conditions, strange attractors, Lyapunov exponents, and why weather forecasts are limited to ~10 days.
ArticleChaos Theory
Chaos Theory & the Butterfly Effect: Lorenz Attractors Explained
Chaos theory explained — sensitive dependence, the Lorenz attractor, Lyapunov exponents, fractal dimension, and why long-range prediction is impossible.
ArticleComplex Systems
Sandpile Model & Self-Organised Criticality
The sandpile model explains self-organised criticality: how systems naturally tune themselves to a critical state with avalanches of all sizes.
ArticleChaos Theory
Rössler Attractor: Spiral Chaos & Bifurcation
A deep dive into the Rössler attractor: the 3D ODE system, spiral vs screw chaos, period-doubling bifurcation, and comparison with Lorenz.
ArticleMathematical Biology
Lotka–Volterra Equations — Predator–Prey Population Cycles
Lotka–Volterra predator–prey equations explained: ODE derivation, equilibria, stability analysis, phase portrait, and full JavaScript RK4 implementation.
ArticleChaos Theory
Lyapunov Exponents: Measuring Chaos in Dynamical Systems
A rigorous guide to Lyapunov exponents — definition, spectrum, Wolf-Swinney-Vastano algorithm, and real-time computation for the logistic map and Lorenz system.
ArticleAstrophysics
The Restricted Three-Body Problem — Chaos in Celestial Mechanics
Explore chaotic dynamics in the restricted three-body problem: Lagrange points, sensitive dependence on initial conditions, and orbital resonance.
ArticleDynamical Systems
Takens' Theorem: Attractor Reconstruction from a Time Series
How to reconstruct a strange attractor from a single scalar measurement using delay embedding, false nearest neighbours, and the Rosenstein algorithm.
ArticleStatistical Physics
Percolation Theory — Phase Transitions in Disordered Systems
Percolation theory explains how connectivity emerges in disordered systems, modelling phase transitions and critical thresholds.
ArticleStatistical Physics
Phase Transitions — Ehrenfest Classification, Ising Model, and Critical Exponents
A complete guide to phase transitions: Ehrenfest classification, order parameters, the 2D Ising model, and critical exponents.
ArticleChaos Theory
Poincaré Sections: Mapping Chaos onto a Plane
Poincaré sections reduce continuous dynamical systems to discrete maps, revealing fixed points, KAM tori, cantori, and period-doubling islands.
ArticleStatistical Physics
Statistical Mechanics — From Atoms to Thermodynamics
Microstates, Boltzmann entropy, Maxwell-Boltzmann distribution, phase transitions, and the partition function explained.
ArticleStatistical Physics
Statistical Mechanics — Boltzmann, Entropy & Phase Transitions
How microscopic states give rise to thermodynamic laws: entropy S=k_B·ln(Ω), partition function, Ising model, critical exponents and universality classes.

🧬 Cellular Automata

8 articles
ArticleCellular Automata
Conway's Game of Life — Maths and Patterns
B3/S23 rules, Gosper glider gun, pulsar, HighLife. Complexity from simplicity.
ArticleChemistry
Reaction-Diffusion and Turing Patterns
Gray-Scott system, F and k parameters, zebra stripes, tiger spots — morphogenesis in JavaScript.
ArticleCellular Automata
3D Cellular Automata — Voxel Life, 3D Neighbourhoods & Volumetric Rendering
Cellular automata extended into the third dimension: 3D Moore and von Neumann neighbourhoods, voxel life rules like 4555 and Amoeba, sparse octree…
ArticleCellular Automata
Wolfram's Rule 110 — The Simplest Turing-Complete Automaton
Rule 110: an eight-bit lookup table on a one-dimensional binary tape that is proven Turing-complete. Covers the elementary cellular automaton framework…
ArticleCellular Automata
Cyclic Cellular Automata: Spiral Waves and Self-Organisation
Cyclic cellular automata self-organise into rotating spiral waves from random noise, via the Greenberg-Hastings model and phase transitions.
ArticleEmergent Behavior
Langton's Ant — Emergence from Two Simple Rules
Two rules on a grid that produce chaos, then an unexpected highway — the algorithm, emergent behaviour, Turmite generalisations, and JavaScript implementation.
ArticleCellular Automata
Wolfram's Elementary Cellular Automata — 256 Rules and the Edge of Computation
A complete guide to Wolfram's 1D elementary cellular automata: the 256 rules, four complexity classes, and Rule 110 Turing completeness.
ArticleCellular Automata
Wolfram Cellular Automata — Rules, Complexity Classes & Conway's Game of Life
Cellular automata from first principles: 256 elementary rules, four complexity classes, Rule 110 universality, and Conway's Game of Life.

🔭 Astrophysics

29 articles
ArticleAstronomy
Planetary Orbits and Kepler's Laws
Kepler's three laws, gravitational parameter μ, Kepler's equation. Three.js implementation.
ArticleAstrophysics
Spiral Arms of Galaxies
Density wave theory, logarithmic spiral, procedural generation of 80k stars.
ArticleAstrophysics
Hohmann Transfer Orbit
Hohmann transfer orbits: vis-viva equation, two-impulse delta-v, bi-elliptic comparison, plane changes, and propellant mass calculations for…
ArticleAstrophysics
Yarkovsky and YORP Effect — How Sunlight Nudges Asteroids
How does absorbed and re-radiated sunlight slowly change an asteroid's orbit and spin? Learn the physics of the Yarkovsky effect (diurnal and seasonal…
ArticleAstrophysics
Binary Star Systems — Two-Body Orbits, Roche Lobes & Three.js
How binary stars orbit each other: the two-body problem, mass ratios, Roche lobes and mass transfer, eclipsing light curves, and how to simulate a binary…
ArticlePlanetary Science
Impact Craters: The Physics of Hypervelocity Collisions
How impact craters form: contact and compression, shock waves, the excavation flow, crater collapse, Pi-group scaling laws, simple vs complex craters…
ArticlePlanetary Science
Volcanism and Hotspots: Mantle Plumes and the Hawaiian-Emperor Chain
Why volcanoes form far from plate boundaries: mantle plumes, the Rayleigh-Taylor instability, the Hawaiian-Emperor seamount chain, age-progression…
ArticleAstrophysics
Gravitational Waves — Ripples in Spacetime
How gravitational waves are generated, what LIGO measures, and the physics behind the quadrupole formula, GW150914, GW170817, and multi-messenger astronomy.
ArticleCosmology
Dark Matter & Dark Energy — The Invisible Universe
What is dark matter and dark energy? Evidence from rotation curves, gravitational lensing, the CMB, and cosmic acceleration.
ArticleCosmology
Big Bang Cosmology — The First 380,000 Years
How the universe began and evolved: cosmic inflation, Big Bang nucleosynthesis, the CMB, and the ΛCDM model.
ArticleAstrophysics
Black Holes — Where Physics Breaks Down
How black holes form: Schwarzschild radius, photon spheres, Hawking radiation, and the Event Horizon Telescope image.
ArticleSpace & Satellite Tech
How GPS Works — Trilateration, Atomic Clocks, and Relativity
GPS uses timing signals from 4+ satellites to pinpoint location. Without Einstein's relativity corrections, it would drift 10 km per day.
ArticleAstrophysics
How Many Stars Are There? — Counting the Universe
About 5,000 stars visible to the naked eye. 200–400 billion in our galaxy. 2 trillion galaxies. How do astronomers count what they cannot visit?
ArticleAstrodynamics
Kepler Orbital Elements — a, e, i, Ω, ω, ν Explained
The six Keplerian orbital elements explained: semi-major axis, eccentricity, inclination, RAAN, argument of periapsis, true anomaly, plus Kepler's equation.
ArticleAstrodynamics
Lagrange Points — L1–L5, JWST, SOHO and Trojan Asteroids
What are the five Lagrange points, why are L4/L5 stable but not L1-L3, and how do JWST, SOHO and DSCOVR use them? Includes the restricted three-body problem.
ArticlePhysics & Cosmology
General Relativity — Curved Spacetime & Gravity
Einstein's general relativity: equivalence principle, metric tensor, geodesics, Schwarzschild solution, time dilation, and black holes.
ArticleAerospace Engineering
Re-entry Heat Shield Physics — Ablation, Plasma, Survival
How do spacecraft survive re-entry? The Chapman formula for stagnation heat flux, ablative materials, ballistic coefficient, and TPS designs explained.
ArticleAstrophysics
What Is a Black Hole? — Gravity, Event Horizons and Time
A kid-friendly guide to black holes: why nothing escapes, the event horizon, time dilation, Hawking radiation and the nearest black hole.
ArticlePhysics
What Is Gravity? — Newton, Einstein and Curved Spacetime
From Newton's inverse-square law to Einstein's curved spacetime — what gravity really is, why planets orbit, and how black holes fit in.
ArticleAstrophysics
The Edge of the Solar System
Where the solar system ends — the heliosphere, termination shock, heliopause, Oort Cloud, and Voyager 1's interstellar crossing.
ArticleAstrodynamics
Orbital Transfers — Hohmann, Bi-Elliptic & Gravity Assist
How spacecraft change orbits: Hohmann transfer, bi-elliptic transfer, gravity assist manoeuvres, and the Oberth effect, via the vis-viva equation.
ArticleAstrodynamics
Orbital Velocity — Circular, Escape, and Transfer Orbits
First and second cosmic velocities, orbital speed formula, Hohmann transfer, and geostationary orbit, explained with derivations and worked examples.
ArticleAerospace Engineering
Tsiolkovsky Rocket Equation
Tsiolkovsky rocket equation: derivation from Newton's laws, specific impulse, staging, gravity losses, and the math behind reaching orbit.
ArticleAerospace Engineering
Tsiolkovsky Rocket Equation & Delta-V Budget
Understand the Tsiolkovsky rocket equation, specific impulse, delta-V budgets, staging, and why every kilo of payload costs kilos of fuel.
ArticleAstrophysics
Stellar Evolution — From Nebula to Supernova and Beyond
How stars are born, spend billions of years on the main sequence, and end as white dwarfs, neutron stars or black holes. Includes the HR diagram and nucleosynthesis.
ArticleAstrophysics
Stellar Interior Structure — How Stars Support Their Own Weight
Hydrostatic equilibrium, the Lane-Emden equation, polytropic models, opacity, and radiative vs convective energy transport in stellar interiors.
ArticlePlasma Physics
Plasma and MHD — Magnetohydrodynamics
Plasma physics and magnetohydrodynamics: plasma parameters, Alfvén waves, ideal MHD equations, and magnetic confinement, visualised with WebGL shaders.
ArticlePlasma Physics
Plasma Physics: The Fourth State of Matter
Plasma physics explained — ionisation, Debye shielding, plasma frequency, MHD, fusion confinement, and industrial applications.
ArticlePlasma Physics
Plasma Waves: Langmuir Oscillations and Landau Damping
Why plasma rings like a bell: plasma frequency, Debye screening, Bohm-Gross dispersion, Landau damping, and Alfvén waves.

📐 Mathematics

40 articles
ArticleProcedural Generation
Perlin Noise and fBm
Gradient noise, octaves, fractional Brownian motion. Terrains, clouds, textures.
ArticleGeometry
Voronoi Diagrams
Fortune's algorithm, Delaunay triangulation, applications in physics and terrain generation.
ArticleFractals
Fractal Geometry and Dimension
Mandelbrot set, Hausdorff fractal dimension, IFS iterated function systems.
ArticleMathematics
Central Limit Theorem — Why Averages Follow a Bell Curve
The Central Limit Theorem explained mathematically: characteristic functions, convergence rate, the Galton board, sampling distributions, and why CLT…
ArticleProbability
Poisson Process and Queuing Theory — Modelling Random Arrivals
How the Poisson process models random arrivals, the exponential inter-arrival distribution, Little's Law, and the M/M/1 and M/M/c queuing models — with…
ArticleAlgorithms
Max-Flow and Network Flows: How Ford-Fulkerson Works
How maximum flow algorithms work — Ford-Fulkerson, Edmonds-Karp, residual graphs, augmenting paths, the max-flow min-cut theorem, and applications in…
ArticleNetwork Science
Network Robustness to Attacks — Percolation, Hubs, and Cascading Failure
Why scale-free networks like the internet survive random failures but collapse under targeted attacks. Percolation theory, degree distribution, giant…
ArticleProcedural Generation
Wave Function Collapse for Procedural Generation
How to build a practical Wave Function Collapse pipeline for procedural levels: tile adjacency extraction, entropy-driven cell selection, constraint…
ArticleMathematics
Golden Ratio & Fibonacci: Phyllotaxis, Continued Fractions & Spirals
From Fibonacci numbers to the golden ratio φ: continued fractions, phyllotaxis, optimal packing, Binet's formula, Zeckendorf's theorem, and logarithmic spirals.
ArticleGeometry
Hyperbolic Geometry — When Parallel Lines Diverge
Explore the Poincaré disk, Gaussian curvature K=-1, Escher's Circle Limit prints, hyperbolic trigonometry, and applications in network science.
ArticleStatistics
Hypothesis Testing — p-values, Type I/II Errors, and Statistical Power
The logic of null hypothesis significance testing: p-values, Type I/II errors, statistical power, effect sizes, t-tests, and the replication crisis.
ArticleComputational Geometry
Bézier Curves and Splines: Mathematics of Smooth Design
De Casteljau's algorithm, Bernstein polynomials, cubic splines, and continuity conditions behind fonts, animation, and CAD.
ArticleMathematical Biology
Fibonacci Numbers in Nature — Spirals, Flowers & the Golden Ratio
Fibonacci numbers appear everywhere in nature: sunflower seeds, pinecone spirals, nautilus shells, and galaxy arms via phyllotaxis.
ArticleGraph Theory
Four-Color Theorem — Graph Coloring and the Computer-Assisted Proof
Any planar map can be colored with at most four colors so no adjacent regions share one — history, computer proof, and graph coloring algorithms.
ArticleProbability Theory
Bayes' Theorem in Practice — Prior, Likelihood, Posterior
Bayes' theorem from first principles: conditional probability, updating beliefs with evidence, conjugate priors, and Bayesian vs frequentist stats.
ArticleStatistics
Bootstrap Resampling: Statistical Inference Without Assumptions
Bootstrap resampling lets you estimate confidence intervals and standard errors for any statistic without assuming a parametric distribution.
ArticleMathematics
Continued Fractions & the Golden Ratio
Continued fractions reveal why the golden ratio is the most irrational number. Explore phi, convergents and how nature exploits this in plant growth.
ArticleComputational Mathematics
Linear Algebra for Simulations: Sparse Solvers, Decompositions & Eigenvalues
The linear algebra toolkit for physics simulations: sparse matrix formats, direct and iterative solvers, preconditioners, eigenvalue algorithms, and SVD.
ArticleComplex Analysis
Complex Functions and Domain Colouring: Visualising the Invisible
How domain colouring maps complex functions to colour, revealing poles, zeros, branch cuts, and the hidden geometry of the complex plane.
ArticleCryptography
RSA Encryption: The Mathematics of Large Primes
RSA secures billions of internet connections daily. Learn the number theory: Euler's totient, modular exponentiation, and why factoring is hard.
ArticleProbability & Statistics
Random Walks & Brownian Motion: From Pollen to Finance
Random walks explained — Brownian motion, diffusion, Monte Carlo, and applications in physics, biology, and finance, with the math behind each step.
ArticleMathematics
What Is a Fractal? Self-Similarity & Infinite Complexity
Fractals are infinitely detailed patterns that look the same at every scale. Learn self-similarity, the Mandelbrot set, and fractals in nature.
ArticlePhysics
What Is Symmetry? — From Snowflakes to Physics Laws
Symmetry is everywhere — in flowers, crystals, and the laws of physics. Discover why scientists use it to unify the forces of nature.
ArticleFractal Mathematics
Mandelbrot Set Algorithms: Escape Time, Distance Estimation & GPU Rendering
Deep dive into Mandelbrot set algorithms — escape-time iteration, smooth colouring, period checking, distance estimation, and massively parallel GPU rendering.
ArticleStochastic Processes
Markov Chains & Random Walks — Stochastic Processes Explained
Markov chains explained: transition matrices, steady-state distributions, PageRank, gambler's ruin, absorbing chains, and random walks with JavaScript code.
ArticleMathematics
Spirograph Mathematics — Hypotrochoids, Epitrochoids & Cycloids
Spirograph mathematics explained: hypotrochoids, epitrochoids and cycloids, their parametric equations and gear ratios.
ArticleMathematics
Quaternions Without Fear — Gimbal Lock, SLERP & Rotations
Quaternions from Hamilton's algebra: complex numbers in R4, rotation representation, gimbal lock, SLERP for smooth animation, and JS implementation.
ArticleAlgorithms
Strassen's Matrix Multiplication — From O(n³) to Sub-Cubic Algorithms
How Strassen's algorithm multiplies matrices in O(n^2.807) instead of O(n³), via divide-and-conquer and the 7-multiplication trick.
ArticleComputer Science
Maze Generation Algorithms — DFS, Prim's, Wilson's and More
How maze generation algorithms work: recursive backtracking DFS, Prim's MST, Wilson's loop-erased walk, Aldous-Broder and Eller's algorithm.
ArticleComputational Statistics
Monte Carlo Methods — Solving Problems with Random Sampling
Estimating π, numerical integration, variance reduction, importance sampling, and MCMC applications in physics, finance and ML.
ArticleComputational Geometry
Origami Mathematics: The Hidden Geometry of Paper Folding
The Huzita-Hatori axioms, why folding can trisect an angle when compass and straightedge cannot, Miura-ori, rigid origami, and real engineering applications.
ArticleNumber Theory
Numbers & Spirals — Number Theory in Pixels
Number theory visualized: Sieve of Eratosthenes, Ulam spiral, prime-counting function, Fibonacci, and golden-angle sunflower spirals.
ArticleNumerical Methods
Numerical Differentiation & Integration: Finite Differences, Gauss Quadrature
A complete guide to finite differences, Richardson extrapolation, Newton-Cotes rules, Gaussian quadrature, and adaptive integration.
ArticleNumerical Methods
Numerical ODE Methods: RK4, Adaptive Steps & Stiff Systems
A guide to integrating ODEs numerically — Euler, RK4, Dormand-Prince RK45, Adams-Bashforth, symplectic integrators, and stiff solvers.
ArticleNumerical Methods
ODE Solvers Compared: Euler, RK4, Verlet, Adaptive Methods
A practical comparison of physics integrators — Euler, symplectic Euler, RK4, Leapfrog/Verlet — with stability and accuracy tradeoffs.
ArticleNumerical Methods
ODE Solvers: Euler, RK4, and Leapfrog Compared
Why does your physics sim explode? Euler, Runge-Kutta RK4, and Leapfrog integrators explained — stability, accuracy, energy conservation.
ArticleNumerical Methods
Newton's Method & Square Roots — Quadratic Convergence and the Fast Inverse Sqrt
Newton-Raphson root finding, quadratic convergence proof, the Babylonian method for square roots, and the legendary Quake III fast inverse sqrt hack.
ArticleMathematics
Spirographs, Hypotrochoids & Epitrochoids: The Maths of Rolling Circles
The complete maths of spirograph curves — hypotrochoids, epitrochoids, cycloids, Lissajous figures, Fourier epicycles, petal counting and gear ratios.
ArticleGeometry & Crystallography
Penrose Tiling & Quasicrystals — Aperiodic Order
Penrose tiling reveals aperiodic order: patterns that never repeat yet follow strict rules, with quasicrystals and five-fold symmetry.
ArticleClassical Mechanics
Optimal Throwing Angle — From 45° in Vacuum to Real Projectile Physics
Why the optimal launch angle is 45° only in vacuum, how drag and the Magnus effect change it, and the math of maximizing range in real sports.

💻 Computer Graphics

30 articles
ArticleRendering
Ray Tracing from Scratch
Rays, sphere/triangle intersection, shadows, reflections, BVH acceleration.
ArticleGLSL
Ray Marching and SDF
Signed Distance Functions, sphere-tracing, ambient occlusion, soft shadows in GLSL.
ArticleShaders
Procedural Textures in GLSL
FBM, Worley noise, marble, wood, reptile skin. All using maths in the shader.
ArticleOptics
Holography and Coherent Light: Why Lasers Make Holograms Possible
Holograms only work because laser light is coherent. Explore temporal and spatial coherence, coherence length, fringe visibility, speckle, and why…
ArticleOptics
Nonlinear Optics: How Intense Light Bends Its Own Rules
When light is intense enough, materials no longer respond in proportion to the field — they generate new colours, focus themselves, and let one beam…
ArticleElectromagnetics
The FDTD Method — Simulating Maxwell's Equations on a Grid
How the Finite-Difference Time-Domain method solves Maxwell's equations directly: the Yee grid, leapfrog time-stepping, the Courant stability limit…
ArticleElectromagnetics
Antennas and Radiation — From the Hertzian Dipole to Phased Arrays
How antennas radiate electromagnetic energy: the Hertzian dipole, near and far fields, radiation pattern and directivity, radiation resistance, the…
ArticleComputer Graphics
Instanced Rendering & LOD: Draw Millions of Objects at 60fps
How instanced rendering and LOD work: GPU draw-call batching, gl_InstanceID, frustum culling, discrete vs continuous morphing LOD.
ArticleReal-Time Graphics
Fluid Rendering in Games — Heightmap Method
Real-time fluid rendering for games using the heightmap shallow-water method, Gerstner waves, WebGL foam shaders, and screen-space reflections.
ArticleFractal Geometry
3D Fractals: Mandelbulb, Menger Sponge & Distance-Field Rendering
Explore 3D fractals: the Mandelbulb power-8 formula, Menger sponge construction, ray-marching signed distance fields, and orbit-trap colouring.
ArticleComputer Graphics
BVH: Bounding Volume Hierarchy for Ray Tracing & Collision Detection
How Bounding Volume Hierarchies accelerate ray tracing and collision detection — AABB trees, SAH construction, GPU BVH, and TLAS/BLAS.
ArticleGraphics Mathematics
Linear Algebra for 3D Graphics: Vectors, Matrices, Quaternions
A thorough guide to linear algebra for 3D graphics — vector operations, matrix transforms, homogeneous coordinates, quaternion rotations, and GPU math.
ArticleComputer Graphics
Introduction to GLSL Shaders — Write Your First GPU Program
Learn GLSL from scratch: the GPU rendering pipeline, vertex and fragment shaders, uniforms, SDFs, and procedural animation.
ArticlePhysics Simulation
Cloth Simulation via Verlet Integration
Cloth simulation with particles and springs: Verlet integration, structural and shear constraints, sphere collisions and self-intersection.
ArticleGame Physics
Collision Detection — BVH, SAT, GJK Explained
How collision detection works in real-time physics engines: broad phase BVH/AABB trees, narrow phase SAT and GJK, and EPA for contact points.
ArticleReal-Time Rendering
Real-Time Denoising: SVGF, A-SVGF, DLSS & ReLAX
How real-time ray tracing denoisers reconstruct clean images from noisy path-traced samples using SVGF, A-SVGF, DLSS, and ReLAX.
ArticleReal-Time Rendering
ReSTIR: Reservoir-based Spatiotemporal Importance Resampling
How ReSTIR renders global illumination in real time via weighted reservoir sampling, spatial/temporal reuse, and ReSTIR DI/GI/PT variants.
ArticleProcedural Graphics
L-Systems & Procedural Plants: Grammar Theory to 3D Trees
How L-systems work: rewriting grammars, turtle graphics, stochastic and context-sensitive rules, and generating fractal plants and trees for games.
ArticleComputer Graphics
Marching Cubes — Extracting Isosurfaces from Volumetric Data
How the marching cubes algorithm extracts triangular meshes from scalar volumetric fields: lookup tables, trilinear interpolation, normals, and MRI/fluid applications.
ArticleComputer Graphics
Material Point Method (MPM): Snow, Sand & Fracture Simulation
A deep-dive into MPM, the hybrid particle-grid technique behind Disney's Frozen snow, soft bodies, fracture, and granular materials.
Article3D Graphics & Geometry
Parametric Surfaces in Three.js — Torus, Hyperboloid & Normal Mapping
Parametric equations for torus, hyperboloid and Klein bottle; building BufferGeometry in Three.js, computing normals, and normal-map shading.
ArticleRendering Algorithms
Path Tracing — Physically Correct Rendering
Monte Carlo integration, BSDF importance sampling, cosine-weighted hemisphere sampling, Russian roulette termination, and a progressive WebGL path tracer.
ArticlePhysics-Based Animation
Position Based Dynamics (PBD): Cloth, Soft Bodies & Constraints
How PBD simulates cloth, soft bodies, and fluids — constraint projection, distance and bending constraints, the PBD loop, and XPBD extensions.
ArticleRendering Algorithms
Physically Based Rendering (PBR) — BRDF, Metalness & IBL
The physics and maths of PBR: the rendering equation, microfacet BRDFs, GGX distribution, Fresnel-Schlick, metalness/roughness workflow, and IBL in GLSL.
ArticleRendering Algorithms
Physically Based Rendering (PBR): Theory and Practice
A comprehensive guide to PBR — the rendering equation, microfacet theory, Cook-Torrance BRDF, metalness workflow, IBL, and implementing PBR in WebGL/GLSL.
Article3D Graphics Programming
Three.js Particle System Tutorial — 100k Particles in the Browser
Build a 100,000-particle system in Three.js using BufferGeometry and Float32Array for zero garbage-collection pressure. Includes performance tips.
ArticleComputer Graphics
Volumetric Rendering — Clouds, Fog & Atmospheric Scattering
How volumetric rendering works: ray marching through participating media, the Beer-Lambert law, phase functions, and how games render clouds and god rays.
ArticleComputer Graphics
WebGL2 Advanced: VAO, Transform Feedback & GPGPU Ping-Pong
A deep dive into advanced WebGL2 features: Vertex Array Objects, Transform Feedback for GPU particle systems, GPGPU ping-pong framebuffers, and float textures.
ArticlePhysics Simulation & Graphics
Position-Based Dynamics — Real-Time Cloth, Ropes and Soft Bodies
How PBD enables stable real-time cloth, rope, and soft-body simulation: constraint projection, XPBD compliance, and GPU parallelism.
ArticleProcedural Generation
Wave Function Collapse Algorithm
How the Wave Function Collapse algorithm generates coherent procedural patterns and textures from local adjacency constraints, inspired by quantum mechanics terminology.

🤖 Robotics & Control

12 articles
ArticleRobotics
Denavit–Hartenberg Parameters: The Robot Arm Convention Explained
A complete guide to Denavit–Hartenberg (DH) parameters — link length a, twist α, offset d, joint angle θ — the four-number convention every robot…
ArticleControl Theory
PID Controller: From Drone to Thermostat
PID controllers are the most widely used feedback control algorithm in engineering. Learn how proportional, integral, and derivative terms work together…
ArticleRobotics
SLAM: Mapping and Localization — How Robots Find Their Place
Simultaneous Localization and Mapping (SLAM) explained: probabilistic state estimation, EKF-SLAM, particle filters, graph-based SLAM, loop closure, and a…
ArticleRobotics & Animation
IK FABRIK: Inverse Kinematics from Scratch in JavaScript
FABRIK inverse kinematics: link chains, iterative forward and backward passes, joint angle limits, and a live canvas demo in JavaScript.
ArticlePathfinding Algorithms
Dijkstra and A*: Shortest Path Algorithms Explained
How Dijkstra's algorithm and A* search work — priority queues, relaxation, heuristic admissibility, and applications in GPS and game AI.
ArticlePathfinding Algorithms
A* Pathfinding Algorithm — From Theory to JavaScript
A* search algorithm explained: f(n) = g(n) + h(n), heuristic functions, open/closed sets, grid encoding, with a full JavaScript implementation.
ArticleAutonomous Vehicles
How Autonomous Vehicles Work — Sensors, Perception, and Path Planning
How self-driving cars sense and navigate: LiDAR, cameras, radar, SLAM, object detection, motion planning, and SAE autonomy levels.
ArticleRobotics
Forward & Inverse Kinematics for Robot Arms
Forward and inverse kinematics from first principles: DH parameters, transformation matrices, Jacobian method, CCD, and FABRIK applied to robotic arms.
ArticleMechanical Engineering
Gear Trains & Mechanisms: Torque, Ratios, Planetary Gears
How gear trains work — ratios, efficiency, spur/helical gears, involute profile, planetary epicyclic gears, and worm drives.
ArticleRobotics Algorithms
RRT Path Planning — Rapidly-Exploring Random Trees
RRT and RRT* path planning algorithms: state-space trees, bias toward goal, asymptotic optimality, and a JavaScript implementation for robotics.
ArticleControl Systems
Modern Control Theory — State Space, LQR, and Observers
State-space representation, controllability and observability, pole placement, the LQR controller, and Kalman filter integration.
ArticleEstimation Theory
Kalman Filter Explained — Optimal State Estimation
The Kalman filter fuses noisy sensor data with a model prediction to get the best possible state estimate — predict-update cycle, gain, EKF, and UKF.

🏗️ Structural & Thermal

15 articles
ArticleStructural Mechanics
Finite Element Method in Structural Mechanics: Trusses, Beams & Frames
How the finite element method models trusses, beams and frames: the direct stiffness method, Euler-Bernoulli beam elements, assembly of global stiffness…
ArticleStructural Mechanics
Fracture Mechanics — When Materials Fail
Stress intensity factors, Griffith's criterion, fatigue crack growth via the Paris law, and a browser-based fracture simulation using Extended FEM…
ArticleThermodynamics
Entropy & the Second Law of Thermodynamics
Explore Boltzmann entropy S=k_B·ln(W), macrostates vs microstates, irreversibility, the arrow of time, Maxwell's demon, and the heat death of the universe.
ArticleThermodynamics
Heat Transfer: Conduction, Convection & Radiation
Fourier's law of conduction, Newton's law of cooling, Stefan-Boltzmann radiation and the heat diffusion PDE, with JavaScript implementations and demos.
ArticleMaterials Science
Dislocations: How Crystals Deform Plastically
Dislocations in crystalline materials — edge and screw types, Burgers vector, slip systems, Taylor hardening, and dislocation density.
ArticleMaterials Science
BCC, FCC & HCP — Crystal Structures of Metals
How atoms pack in BCC, FCC, and HCP crystal structures: coordination numbers, packing factors, Miller indices, and slip systems.
ArticleMetallurgy
Binary Alloy Phase Diagrams — From Liquidus to Eutectic
Binary alloy phase diagrams map liquidus, solidus and eutectic lines to predict which phases form in a metal mixture.
ArticleComputational Mechanics
Finite Element Method Explained: Meshing, Solving & Results
FEM explained — mesh generation, shape functions, assembly of stiffness matrices, boundary conditions, convergence, from structural to CFD analysis.
ArticleComputational Mechanics
Finite Element Method (FEM) Explained Simply
The Finite Element Method made accessible — weak forms, mesh generation, shape functions, stiffness matrices, and engineering applications.
ArticleStructural Engineering
Finite Element Method — Structural Analysis
How FEM turns continuous elasticity PDEs into a computable stiffness matrix, from weak forms to plane-stress simulation.
ArticleMaterials Science
Crystal Dislocations & Plastic Deformation
Crystal dislocations drive plastic deformation in metals: how line defects glide, why they explain strength, work-hardening, and ductility in real materials.
ArticleStructural Engineering
Geodesic Domes — Geometry, Strength & Fuller's Vision
How Buckminster Fuller turned icosahedra into efficient structures: subdivision, Euler's formula, great circle arcs, and tensegrity.
ArticleStructural Engineering
Material Fatigue: Why Things Break Under Repeated Loading
Material fatigue explained — S-N curves, crack initiation, crack growth (Paris law), cumulative damage (Miner's rule), and fatigue life prediction.
ArticleThermal Engineering
Stirling Engine — Thermodynamic Cycles, Carnot Efficiency and Regeneration
How the Stirling engine achieves Carnot efficiency via isothermal/isochoric processes, the regenerator, alpha/beta/gamma configurations, and real-world applications.
ArticleApplied Physics
Hyperloop & Maglev: Physics of Ultra-Fast Ground Transport
The physics behind maglev trains and Hyperloop — magnetic levitation, linear induction motors, near-vacuum tubes, and transonic aerodynamic drag.

🧪 Chemistry & Materials

12 articles
ArticleBiochemistry
Bioluminescence: When Life Glows in the Dark
The chemistry of living light: luciferin and oxygen reactions, quantum yield in fireflies, and how GFP transformed bioimaging.
ArticleAdvanced Materials
Advanced Materials: Graphene, Carbon Nanotubes, and Aerogels
The science behind wonder materials: graphene's Dirac cone, carbon nanotube chirality, aerogel insulation, and metamaterial negative refraction.
ArticleMaterials Science
How Crystals Form — Nucleation, Lattices, and DLA
How crystals form from nucleation and growth: supersaturation, Bravais lattices, snowflake branching, diffusion-limited aggregation, and crystal symmetry.
ArticleMaterials Science
Crystal Structure: How Atoms Arrange Themselves
Crystal structures explained — unit cells, Bravais lattices, Miller indices, X-ray diffraction (Bragg's law), defects, and why structure determines material properties.
ArticleStructural Biology
X-Ray Crystallography — How We See Atoms
Bragg's law, crystal lattices, Miller indices, the structure factor, the phase problem, and how protein crystallography revealed over 100,000 molecular structures.
ArticleMolecular Physics
Lennard-Jones Potential — The Foundation of Molecular Dynamics
The Lennard-Jones 12-6 potential explained: derivation, equilibrium distance, well depth, reduced units, cutoff radius, and its role in molecular dynamics.
ArticleColloid Chemistry
Colloid Science: Why Milk Doesn't Separate (Usually)
DLVO theory explains why colloids like milk stay stable: van der Waals attraction vs electrostatic repulsion, zeta potential, and salt destabilisation.
ArticleCombustion Chemistry
Combustion Chemistry: The Science of Flames and Fire
Explore combustion chemistry — fuel oxidation kinetics, flame structure, adiabatic temperatures, and radical chain reactions that sustain fire.
ArticleChemistry
Why Ice Floats on Water — Anomalous Density Explained
Most liquids are denser than their solid form, but water is different. Discover why hydrogen bonds make ice less dense than liquid water.
ArticleMaterials Science
Why Is Every Snowflake Unique? — Ice Crystal Formation
No two snowflakes are alike — explore how water molecules, temperature, humidity and fractal branching make each one one-of-a-kind.
ArticleChemistry
Soap & Surfactants: The Physics of Getting Things Clean
How soap works at the molecular level — amphiphilic molecules, micelle formation, surface tension reduction, and CMC.
ArticleChemistry
Van der Waals Equation — Real Gases & Phase Transitions
Explore the van der Waals equation: intermolecular forces, van der Waals constants, critical point, Maxwell construction, and gas liquefaction.

🧬 Life Sciences & Medicine

32 articles
ArticleNeuroscience
Hodgkin-Huxley Neuron — Action Potential from Ionic Currents
The Hodgkin-Huxley model explained: four coupled ODEs, ion channel gating variables m, h, n, RK4 integration, and action potential phases with full code.
ArticleMedicine
Human Microbiome: Trillions of Bacteria Inside You
The human microbiome has ~38 trillion microbial cells. Explore how gut bacteria shape immunity, metabolism, mental health, and disease.
ArticleEndocrinology
Insulin and Diabetes: Glucose Regulation and Disease
How insulin regulates blood glucose — GLUT4 translocation, Type 1 vs Type 2 diabetes, beta cell destruction, and the artificial pancreas.
ArticleCardiac Biophysics
Mathematical ECG and Heart Models — Van der Pol Oscillator and QRS Complex
The mathematics of the heartbeat: SA node automatism, Van der Pol oscillator model, QRS complex generation, and arrhythmia mechanisms.
ArticleMolecular Biology
Epigenetics: How Genes Get Switched On and Off
How environment, diet, and stress change gene expression without altering DNA sequence — methylation, histone modification, and inheritance.
ArticleMolecular Biology
How DNA Works — From Double Helix to Protein
DNA is a molecule that stores the instructions for life. Learn how the double helix encodes genes and how cells convert genes into proteins.
ArticleComputational Neuroscience
FitzHugh-Nagumo Neuron Model — Phase Plane, Excitability, and Action Potentials
The FitzHugh-Nagumo model of neural excitability: phase plane analysis, nullclines, limit cycles, and coupled oscillator synchronisation.
ArticleEcology
Forest Succession: How Ecosystems Rebuild Themselves
From bare rock to old-growth forest: primary vs secondary succession, pioneer species, climax communities, and fire ecology.
ArticleNeuroscience
Neural Action Potential — From Ions to Thought
How neurons fire: Goldman equation, Nernst potential, sodium/potassium channels, the all-or-nothing spike, and the Hodgkin-Huxley model.
ArticleMicrobiology & Evolution
Antibiotic Resistance: Evolution in Real Time
How antibiotic resistance evolves — mechanisms of resistance, mutation rates, horizontal gene transfer, and ESKAPE pathogens.
ArticleMedical Physics
How MRI Works — Nuclear Magnetic Resonance and Medical Imaging
A complete guide to MRI scanners: nuclear magnetic resonance, T1/T2 relaxation, gradient coils, k-space, and image reconstruction via 2-D Fourier transform.
ArticleBiomedical Physics
Blood Flow & Poiseuille's Law
Poiseuille flow in blood vessels: viscosity, resistance, the fourth-power law, laminar vs turbulent blood flow, and cardiovascular pressure.
ArticleBiotechnology
How CRISPR-Cas9 Works — Gene Editing Explained
CRISPR-Cas9 uses a bacterial immune memory to cut DNA at any target sequence. Understand the mechanism, repair pathways, and applications from gene therapy to agriculture.
ArticleBiotechnology
CRISPR-Cas9: Molecular Scissors Explained
How CRISPR-Cas9 gene editing works — guide RNA design, double-strand breaks, NHEJ vs HDR repair, off-target effects, and real-world applications.
ArticleChronobiology
Circadian Rhythms — The Body's Internal Clock
How the 24-hour circadian clock works: the suprachiasmatic nucleus, CLOCK/BMAL1 feedback loops, melatonin, light entrainment, and jet lag.
ArticleGenetics
Cloning Explained: From Dolly to iPSCs
Understanding biological cloning — somatic cell nuclear transfer, Dolly the sheep, reproductive vs therapeutic cloning, iPSCs, and gene cloning with PCR.
ArticleHealth Physics
Radiation Doses: Sieverts, X-rays & Perspective
Radiation is measured in sieverts, but the number alone tells little without context — X-rays, flights, background radiation, and Chernobyl compared.
ArticleNeuroscience
Mathematical Models of Sleep — Process S, Circadian Rhythm and the Two-Process Model
How the two-process model of sleep regulation works: homeostatic sleep pressure (Process S), the circadian clock, and the sleep gate.
ArticleNeuroscience
Sleep Science: Stages, Circadian Rhythm, and Why We Sleep
The neuroscience and physiology of sleep — NREM and REM stages, circadian rhythm, adenosine pressure, and sleep disorders.
ArticleCognitive Science
The Science of Spaced Repetition — Memory, Forgetting, and Optimal Learning
The neuroscience of spaced repetition: Ebbinghaus forgetting curve, SM-2 algorithm, synaptic consolidation, and the testing effect.
ArticleCognitive Science
The Science of Spaced Repetition: Ebbinghaus, SM-2 and Memory
Master spaced repetition with the Ebbinghaus forgetting curve, SM-2 algorithm and active recall for long-term memory.
ArticleNeuroscience
How the Brain Stores Memory
How memory works in the brain — memory stages, hippocampus, LTP and synaptic plasticity, sleep consolidation, and the forgetting curve.
ArticleNeuroscience
How the Visual Cortex Works — Hubel-Wiesel, V1–V5 Hierarchy, and Neural Coding
How the visual cortex processes images: V1 through V5 area hierarchy, Hubel-Wiesel orientation columns, simple/complex cells, and the ventral and dorsal streams.
ArticleMedical Imaging
MRI: How You Get Scanned Without Radiation
How MRI works without radiation — nuclear magnetic resonance, spin physics, T1/T2 relaxation, gradient coils, k-space, and image contrast explained step by step.
ArticleBiology
Mycelium Networks — Nature's Underground Internet
How mycelium networks transport nutrients, carry electrical signals, inspire computing algorithms, and form the Wood Wide Web connecting forest ecosystems.
ArticleNeuroscience
Neural Connectome — C. elegans Network, Hub Neurons, and Rich-Club Topology
The complete wiring diagram of C. elegans: 302 neurons, 7,000 synapses, hub interneurons, rich-club topology, and a force-directed connectome visualisation.
ArticleNeuroscience
Neural Oscillations: The Rhythms of the Brain
Delta, theta, alpha, beta, and gamma brain wave bands, how they arise from coupled neurons, their role in cognition and sleep, and the Kuramoto model.
ArticleNeuroscience
Synaptic Plasticity — Hebb's Rule, LTP/LTD, and Spike-Timing-Dependent Plasticity
A deep dive into synaptic plasticity: Hebb's rule, long-term potentiation/depression, STDP windows, BCM theory, and homeostatic scaling.
ArticleSystems Biology
Systems Biology: Networks, Circuits, and Emergent Life
Gene regulatory networks, protein interaction networks, signalling cascades, feedback motifs, ODE modelling of gene expression, and synthetic biology.
ArticleMedicine & Pharmacology
Pharmacokinetics — ADME, Compartment Models and Drug Half-Life
How drugs move through the body: ADME, one- and two-compartment ODE models, half-life, bioavailability, and loading doses.
ArticleComputational Biology
Protein Folding: The HP Lattice Model Explained
The HP lattice model of protein folding: hydrophobic-polar amino acid sequences, energy landscapes, and a simplified 2D grid approach.
ArticleMathematical Biology
Morphogenesis and Turing Patterns — Reaction-Diffusion Systems
Alan Turing's 1952 reaction-diffusion theory of morphogenesis: activator-inhibitor systems, Turing instability, and animal coat patterns.

🌐 Networks, Society & Finance

18 articles
ArticleCybersecurity
HTTPS & TLS 1.3 Explained: How Secure Connections Work
Explore the TLS 1.3 handshake, certificate validation, ECDHE key exchange, AEAD ciphers, and how HTTPS protects data in transit.
ArticleDistributed Systems
Distributed Consensus: Paxos and Raft Explained
How distributed systems agree on a value despite crashes and network partitions — Paxos, Raft leader election, and log replication.
ArticleNetwork Epidemiology
Epidemic Spreading on Networks: Super-spreaders and Herd Immunity
How diseases spread through contact networks, why super-spreaders dominate outbreaks, how network topology shapes R0, and herd immunity thresholds.
ArticleCryptography & Distributed Systems
How a Blockchain Works — From SHA-256 to Bitcoin
A blockchain is a tamper-proof chain of records secured by cryptographic hashes. Understand proof-of-work, mining, 51% attacks and smart contracts.
ArticleCryptography
How Diffie-Hellman Key Exchange Works — HTTPS Explained
Two strangers share a secret over a public channel without ever transmitting it. Understand Diffie-Hellman with the paint-mixing analogy.
ArticleCryptography
How Encryption Works — From Caesar Cipher to RSA
How encryption works: from the Caesar cipher to symmetric AES and public-key RSA cryptography, and the maths that makes HTTPS unbreakable.
ArticleEconomics & Finance
Financial Contagion — How Bank Failures Cascade
The Eisenberg-Noe model of financial contagion, systemic risk, too-big-to-fail, network topology, the 2008 crisis, and stress testing.
ArticleDistributed Systems
Consistent Hashing — Distributed Load Balancing with Virtual Nodes
How consistent hashing distributes data across distributed caches and databases with minimal remapping on node changes, using ring hash space and virtual nodes.
ArticleFinance & Crypto
DeFi Explained: AMMs, Liquidity Pools & Smart Contracts
Decentralized Finance replaces banks with math. Automated Market Makers, liquidity pools, impermanent loss, and algorithmic lending rates explained.
ArticleGame Theory
Game Theory — Nash Equilibrium, Prisoner's Dilemma and Strategic Interaction
How rational agents make decisions, Nash equilibrium, cooperation vs defection, and applications in economics and biology.
ArticleTraffic Engineering
Roundabouts vs Traffic Lights: Which Is Better?
A data-driven analysis of roundabouts versus signalised intersections — throughput, safety, emissions, and pedestrian access.
ArticleDistributed Systems
Raft Consensus Algorithm — Leader Election and Log Replication
How the Raft consensus algorithm achieves fault-tolerant distributed agreement: leader election, log replication, heartbeats, and comparison with Paxos.
ArticleQuantitative Finance
Markowitz Portfolio Theory: The Efficient Frontier
Harry Markowitz showed diversification reduces portfolio risk. The efficient frontier, minimum variance portfolio, and Sharpe ratio define optimal allocation.
ArticleQuantitative Finance
Options & Hedging: Black-Scholes and the Greeks
Options give the right to buy or sell an asset. Black-Scholes prices them; the Greeks measure risk sensitivity — how Wall Street hedges billion-dollar portfolios.
ArticleTransportation Engineering
Traffic Intersection Optimization: Queue Theory and Signal Timing
How do traffic engineers minimise delay at signalised intersections? Webster's formula, Poisson arrivals, level-of-service, and adaptive control.
ArticleCybersecurity
SQL Injection, XSS & CSRF: Common Web Security Attacks
SQL injection, Cross-Site Scripting, and CSRF are the most common web vulnerabilities — learn how each attack works, real examples, and required defences.
ArticleNetwork Science
Network Science — The Mathematics of Connected Systems
Graph theory, small-world and scale-free networks, clustering, community detection, and the PageRank algorithm explained.
ArticleTraffic Dynamics
Phantom Traffic Jams — Why Congestion Appears from Nowhere
Traffic jams can form and travel backwards on an empty road with no accident or bottleneck — the wave physics behind phantom jams.

🎵 Signals, Sound & Perception

20 articles
ArticleBioacoustics
Echolocation: How Bats and Dolphins See with Sound
The physics of biosonar: range from time of flight, frequency-swept chirps, matched filtering, Doppler compensation, and jamming avoidance.
ArticleSignal Processing
FFT Explained: How the Fast Fourier Transform Works
Why the naive DFT is O(N²), how Cooley-Tukey reduces it to O(N log N), butterfly diagrams, twiddle factors, and real applications.
ArticleOptics & Telecommunications
Fiber Optics: How Light Carries the Internet
A hair-thin glass fiber carries terabits per second across continents — total internal reflection, numerical aperture, and wavelength multiplexing.
ArticleAudio Signal Processing
How Audio Fingerprinting Works: The Shazam Algorithm
How does Shazam identify a song in seconds with background noise? Landmark-based fingerprinting: spectrograms, peak detection, and hashing.
ArticleMedical Physics
How Ultrasound Works — Piezoelectricity, B-mode Imaging and Doppler
How medical ultrasound works: piezoelectric transducers, pulse-echo timing, impedance matching, B-mode imaging, Doppler blood flow, and phased array steering.
ArticleTelecommunications
How WiFi Works — OFDM, Subcarriers and Wireless Physics
How WiFi transmits data: radio waves, 2.4 GHz and 5 GHz bands, OFDM subcarriers, QAM modulation, MIMO antennas, 802.11 frame structure, and interference.
ArticleSignal Processing
Fourier Analysis — Decomposing Any Signal into Sine Waves
The Fourier transform, frequency domain, and FFT — with applications in signal processing, audio and image compression.
ArticleSignal Processing
The Fourier Transform — How It Works and Where It Appears
How the Fourier transform decomposes signals into sine waves, and why it matters for audio, images, and quantum mechanics.
ArticleSignal Processing
The Fourier Transform — From Signals to Spectra
DFT vs FFT, the convolution theorem, Parseval's theorem, and real applications in audio, MRI, JPEG, and radio.
ArticleAcoustics & Signal Processing
Fourier Transform and Sound — DFT, FFT & Spectrograms
The Fourier transform explained through sound: complex exponentials, the DFT, Cooley-Tukey FFT, spectrograms and pitch detection.
ArticleSignal Processing
The Fourier Transform — Decomposing Everything Into Waves
A complete guide to the Fourier transform: periodic signals, complex exponentials, the DFT, Cooley-Tukey FFT, and applications from audio to MRI.
ArticleAuditory Physics
How the Cochlea Hears: Basilar Membrane Resonance
How the cochlea analyses sound: basilar membrane travelling waves, tonotopic mapping, hair cell mechanotransduction, and frequency selectivity physics.
ArticleInformation Theory
Shannon-Nyquist Theorem — The Limits of Information
The Nyquist sampling theorem, aliasing, Shannon channel capacity, information entropy, and the fundamental limits of digital communication.
ArticlePsychoacoustics
Shepard Tone & Auditory Illusions — Pitch Without End
The Shepard tone is an auditory illusion of a pitch that seems to rise or fall forever. Learn how it works and the maths behind it.
ArticleAcoustics
Sound Wave Propagation: How Sound Travels Through Matter
How sound waves travel through different media, covering speed, wavelength, and the physics of acoustic propagation.
ArticleSound & Music
Spectral Synthesis & the Harmonic Series
Spectral synthesis builds sound from the harmonic series, layering overtones to shape timbre, with the maths and applications.
ArticlePsychoacoustics
Psychoacoustics: How We Hear Sound
The science of sound perception — loudness, pitch, critical bands, masking, binaural hearing, localisation, and auditory illusions.
ArticleAcoustics
Timbre: The Colour of Sound
Timbre in acoustics — harmonic series, Fourier decomposition of instrument sounds, ADSR envelopes, formant frequencies, and synthesis methods.
ArticleSignal Processing
Wavelet Transform — The Language of Time and Frequency
Master the wavelet transform: Heisenberg uncertainty in time-frequency analysis, continuous vs discrete transforms, Haar and Daubechies wavelets, and JPEG2000.
ArticleAcoustics & Waves
Standing Waves & Resonance: Normal Modes, Chladni Patterns & FFT
From string harmonics to 2-D Chladni figures — standing waves, normal modes, resonance, and real-time FFT audio analysis.

🌍 Energy, Climate & Earth Science

27 articles
ArticleClimate Science
The Greenhouse Effect — Physics of Global Warming
How greenhouse gases trap infrared radiation, why CO2 matters more than water vapour at the margin, and the physics behind Earth's rising temperature.
ArticleEarth Science
Hurricane Formation: Warm Oceans, Spiral Winds, and the Coriolis Force
How hurricanes form and intensify — warm sea surface temperatures, convection, Coriolis deflection, the eye wall, storm surge, and categories.
ArticleSeismology
Fault Mechanics: From Stress to Earthquake
The physics of earthquakes: elastic rebound, the stick-slip model, Mohr-Coulomb failure, seismic moment, and the Gutenberg-Richter law.
ArticleClimate Science
Earth's Energy Balance — the Physics of Climate
Zero-dimensional energy balance models, Stefan-Boltzmann law, greenhouse forcing, albedo-temperature feedback and tipping points in climate science.
ArticleEnergy Storage
EV Batteries: Why the Battery Is the Bottleneck
Lithium-ion battery chemistry for electric vehicles — energy density, charge rates, degradation mechanisms, thermal management, and solid-state batteries.
ArticleGeophysics
How Earthquakes Happen: Plate Tectonics to Seismic Waves
Earthquake physics explained — tectonic plates, fault mechanics, elastic rebound, P/S/surface waves, magnitude scales, and seismic engineering.
ArticleVolcanology
How Volcanoes Work — Magma, Pressure & Eruption Physics
How do volcanoes erupt? Magma formation, buoyancy-driven ascent, pressure buildup, eruption styles, lava rheology, and pyroclastic flows.
ArticleClimate Science
The Carbon Cycle: Earth's Climate Regulator
How the carbon cycle regulates Earth's climate — from photosynthesis and ocean uptake to permafrost feedbacks and tipping points.
ArticleEarth Science
The Carbon Cycle Explained — Reservoirs, Fluxes and Climate
Carbon moves between five reservoirs through natural and human-driven fluxes — why a 10 GtC/yr emission tips a 200 GtC/yr system into imbalance.
ArticleThermodynamics
Carnot Cycle & Heat Engines
Carnot cycle thermodynamics: four reversible processes, PV/TS diagrams, maximum efficiency, and why no real engine can beat it.
ArticleEarth Science
Earth's Geomagnetic Field: Dynamo, Reversals & Navigation
Earth's geomagnetic field explained — the geodynamo, field structure, polarity reversals, magnetosphere, and space weather.
ArticleGeomorphology
Sand Dune Formation: Physics of Desert Landforms
How barchan and other sand dunes form: aeolian sediment transport, saltation, reptation, avalanching, and the physics of dune migration.
ArticleClimate Science
Arctic Sea Ice: Physics of Freezing and the Albedo Feedback
The physics of Arctic sea ice: Stefan's law for ice growth, the ice-albedo feedback, brine rejection, and the sea-ice tipping point.
ArticleEarth Science
The Physics of Wildfire Spread
How wildfires spread: combustion thermodynamics, the Rothermel fire model, spotting, crown fires, fire weather, and climate change effects.
ArticleRenewable Energy
Wind Turbine Physics: From Betz Limit to Grid Power
The physics of wind turbines — Betz limit, tip-speed ratio, blade aerodynamics, HAWT vs VAWT design, and the power curve with real-world data.
ArticleEnergy Physics
Solar Panels: From Photon to Watt
How solar panels work: the photoelectric effect, p-n junction physics, the Shockley-Queisser limit, and multi-junction cells.
ArticleEnvironmental Science
Microplastics: Where They Come From and Where They End Up
Microplastics contamination explained — sources, transport pathways, detection methods, and health impacts across water, air and food chains.
ArticleEarth Science
Tectonic Plates & Mantle Convection — Learning Materials
How do continents move? Explore the physics of mantle convection, plate tectonics and mesh deformation behind interactive simulations.
ArticleOcean & Climate Science
The Ocean Conveyor Belt: Thermohaline Circulation
How density ρ=ρ0(1−αΔT+βΔS) drives the global ocean conveyor: NADW formation, the Stommel box model, AMOC slowdown, and climate tipping points.
ArticleOcean & Climate Science
Thermohaline Circulation — The Ocean Conveyor Belt and Climate
How thermohaline circulation drives the global ocean conveyor belt: density-driven flow, T-S diagrams, the AMOC, and why its slowdown threatens climate.
ArticleEarth Science
Volcano Eruption Physics: Magma, Pressure & Pyroclastic Flows
Volcano eruption physics: magma composition, viscosity, volatile exsolution, the VEI scale, effusive vs explosive eruptions, pyroclastic flows, and lahars.
ArticleNuclear Physics
Nuclear Fusion: How Stars Burn & Why It's Hard
Fusion powers the Sun at 100 million°C — explore tokamaks, inertial confinement, and the race toward net energy gain on Earth.
ArticleOcean Chemistry
Ocean Acidification — When CO2 Meets Seawater
How CO2 dissolves in seawater to form carbonic acid, and why the resulting pH drop threatens corals, shellfish, and food webs.
ArticleClimate Science
Ocean Currents & Climate: How the Ocean Moves Heat
Surface gyres, the thermohaline conveyor, AMOC, and El Niño — how ocean circulation regulates Earth's climate.
ArticleEnergy Engineering
Nuclear Accidents: Chernobyl, Fukushima & Lessons Learned
Three of the worst nuclear accidents — TMI, Chernobyl, Fukushima — share a pattern: design flaws compounded by human decisions under pressure.
ArticleGeophysics
Seismic Waves — How Earthquakes See Inside the Earth
P-waves, S-waves, surface waves, Snell's law at layer boundaries, the seismic shadow zone, and how seismographs measure earthquake magnitude.
ArticleNuclear Physics
Nuclear Explosion Physics
Fission chain reactions, critical mass, implosion design, fireball stages, and Glasstone scaling laws behind nuclear explosions.

💻 Computing, Quantum & Data Science

51 articles
ArticleComputer Architecture
GPU Parallel Computing — SIMT, Warp Divergence, and the Roofline Model
How GPUs achieve massive parallelism: SIMT execution, warp divergence, shared memory bank conflicts, the roofline model, occupancy, and WebGPU compute shaders.
ArticleMachine Learning
Gradient Descent & Modern Optimisers — Adam, RMSprop, Momentum
Gradient descent is the optimisation engine behind deep learning. Learn how momentum, RMSprop and Adam accelerate training and converge reliably.
ArticleArtificial Intelligence
How AI Thinks: Neural Networks, Training & Inference
How modern AI works — neurons, layers, backpropagation, transformers, attention, and the path from training data to generated text and images.
ArticleInformation Theory
Information Theory — Shannon Entropy and the Limits of Communication
Shannon entropy, channel capacity, data compression, error correction, and applications in cryptography and biology.
ArticleQuantum Physics
Josephson Junction — Quantum Tunnelling Through a Superconducting Barrier
Quantum tunnelling of Cooper pairs through a thin barrier between two superconductors, the governing equations and applications.
ArticleGenerative AI
How AI Generates Images — Diffusion Models Explained
How Stable Diffusion, DALL-E, and Midjourney generate images: forward noise, reverse denoising, U-Net, latent diffusion, and CLIP guidance.
ArticleGame Engine Architecture
Entity Component System — Game Architecture Explained
How Entity Component System (ECS) architecture works: entities, components, systems, archetype storage, and cache efficiency.
ArticleComputer Science Fundamentals
Binary Numbers & IEEE 754 — How Computers Represent Integer and Floating-Point Data
Binary numbers, two's complement, bitwise tricks, and IEEE 754 floating-point representation with NaN and Infinity.
ArticleQuantum Physics
Blackbody Radiation and Planck's Law: Birth of Quantum Theory
Blackbody radiation and Planck's law — the quantum breakthrough that explained the ultraviolet catastrophe.
ArticleInformation Theory
Error Correction Codes: Protecting Data in a Noisy World
Shannon's noisy-channel theorem, Hamming SECDED codes, Reed-Solomon codes, CRC polynomials, LDPC codes, and quantum error correction explained.
ArticleAI & Machine Learning
How ChatGPT Works — Transformers, Attention & Language Models
A precise step-by-step explanation of how ChatGPT works: tokenisation, embeddings, self-attention, transformer blocks, and RLHF fine-tuning.
ArticleComputer Architecture
How a CPU Works: Fetch, Decode, Execute
Modern CPUs execute billions of instructions per second via pipelining, branch prediction, out-of-order execution, and multi-level caches.
ArticleMachine Learning
Backpropagation — the Chain Rule Unwrapped
Deep dive into backpropagation: computational graphs, forward and backward passes, Jacobians, vanishing gradients, and a minimal autograd engine.
ArticleAI & Machine Learning
How Neural Networks Learn — Backpropagation Explained
Forward pass, loss functions, backpropagation and gradient descent — how a neural network adjusts its weights to learn from data, with visual examples.
ArticleElectronics & Computing
How a Transistor Works — From Silicon to CPU
A transistor is a switch made of silicon that controls electrical current. Understand semiconductors, p-n junctions, MOSFETs, and how CPUs are built from them.
ArticleCryptography & Computing
Blockchain & Bitcoin: The Mathematics
The mathematical foundations of blockchain: SHA-256 hashing, Merkle trees, proof of work, ECDSA signatures, and the Byzantine Generals problem.
ArticleQuantum Physics
Bose–Einstein Condensate — The Fifth State of Matter
How quantum statistics, superfluidity, and macroscopic wavefunctions emerge when matter is cooled to 100 nanokelvin.
ArticleDigital Logic
Logic Gates & Boolean Algebra — From Transistors to CPUs
How AND, OR, NOT, and XOR gates work, how De Morgan's laws simplify circuits, and how gates combine into an adder and an ALU — the core of every computer.
ArticleComputer Science
Genetic Algorithms — Evolutionary Optimization in Computer Science
Selection, crossover and mutation operators, fitness landscapes, and applications in optimization and machine learning.
ArticleMachine Learning
K-Means & DBSCAN Clustering
Clustering algorithms compared: K-Means EM iteration, DBSCAN density-reachability, inertia vs silhouette scoring, and JavaScript implementation.
ArticleComputer Vision
Computer Vision Basics: From Pixels to Understanding
How computers see and interpret images — convolutions, CNNs, feature detection, object detection (YOLO), and vision transformers.
ArticleQuantum Physics
Schrödinger Equation & Wave Packets — Quantum Mechanics from First Principles
Time-dependent Schrödinger equation, probability density, particle-in-a-box, quantum tunnelling, uncertainty principle, and wave-packet simulation.
ArticleNeural Networks
Self-Organizing Maps: Topology-Preserving Neural Networks
How Kohonen's self-organizing map learns: competitive learning, the best matching unit, the neighborhood function, and the U-matrix.
ArticleComputer Science Fundamentals
Recursion Explained — Call Stack, Memoization, and Tail Call Optimization
Recursion from first principles: the call stack, base cases, tree recursion, memoization, dynamic programming, and tail call optimization.
ArticleMachine Learning
Reinforcement Learning Explained — Q-Learning, Bellman Equation, DQN
Agent, environment, reward, policy, Q-values, the Bellman equation, Q-learning, and deep RL (DQN) explained with the CartPole example.
ArticleMachine Learning
What Is Machine Learning? Supervised, Unsupervised & Reinforcement
A clear guide to supervised, unsupervised and reinforcement learning — with the bias-variance tradeoff, overfitting, and generalisation.
ArticleMachine Learning
Machine Learning — From Linear Regression to Deep Learning
The mathematical foundations of modern AI: supervised vs unsupervised learning, bias-variance tradeoff, regularisation, CNNs, RNNs, attention, and transformers.
ArticleQuantum Computing
Shor's Algorithm — How Quantum Computing Breaks RSA Encryption
Shor's algorithm explained: quantum period finding, quantum Fourier transform, modular exponentiation, and the timeline to breaking RSA.
ArticleComputer Science
Sorting Algorithms Visualized — Bubble, Merge, Quick, Heap and More
Visual comparison of classic sorting algorithms with complexity analysis, stability, and JavaScript implementations.
ArticleQuantum Computing
Quantum Algorithms: Grover, Shor, and the Quantum Advantage
Grover search, Shor factoring, quantum Fourier transform, variational algorithms (VQE, QAOA), complexity classes, and NISQ-era limitations.
ArticleQuantum Computing
Quantum Computers Simply Explained
Quantum computing for non-physicists — qubits, superposition, entanglement, and why quantum computers solve some problems exponentially faster.
ArticleQuantum Computing
Quantum Computing Basics: Qubits, Superposition & Entanglement
Quantum computing from scratch — what qubits are, how superposition and entanglement work, and what problems quantum computers can solve.
ArticleQuantum Computing
Quantum Computing Explained — No Formulas Required
Superposition, entanglement, and interference: the three ideas behind quantum computing, explained without equations.
ArticleQuantum Mechanics
Quantum Harmonic Oscillator: Energy Levels and Wave Functions
Energy eigenvalues, Hermite polynomials, wavefunctions, zero-point energy, probability density, and the correspondence principle.
ArticleQuantum Mechanics
Quantum Mechanics Interpretations Explained
Copenhagen, Many-Worlds, Pilot Wave, Relational, and QBism — the major interpretations of quantum mechanics compared without the mysticism.
ArticleQuantum Mechanics
Quantum Tunnelling — How Particles Pass Through Walls
How quantum mechanics allows particles to tunnel through energy barriers: Schrödinger equation, WKB approximation, tunnel diodes, and stellar fusion.
ArticleQuantum Algorithms
Quantum Walks — Ballistic Transport vs Classical Diffusion
Quantum walks spread ballistically, not diffusively. Explore how quantum interference reshapes transport and powers algorithms.
ArticleQuantum Computing
Qubit Technologies: Superconducting, Trapped Ion, and Photonic Qubits
Comparison of qubit technologies — transmons, trapped ions, photonic, spin, and topological qubits: coherence times, gate fidelities, and scalability.
ArticleQuantum Computing
Qubits & Quantum Gates — State Vectors, Bloch Sphere and Quantum Circuits
Qubit state vectors, Bloch sphere geometry, Pauli/Hadamard/phase-shift/CNOT gates, and quantum circuit simulation in JavaScript.
ArticleComputer Networking
TCP/IP Explained — How Data Travels the Internet
How does the internet really work? TCP handshake, IP routing, encapsulation, NAT and congestion control explained with diagrams.
ArticleMachine Learning
Transformer Architecture Explained — Attention Is All You Need
How the Transformer neural network works: self-attention, multi-head attention, positional encoding, and why it replaced RNNs.
ArticleElectronics History
How the Transistor Changed Everything: From Vacuum Tubes to 2 nm
The transistor is the most manufactured object in history. How it was invented, how it works, and how Moore's Law drove 60 years of miniaturisation.
ArticleComputer Graphics
WebGPU Compute Shaders: General GPU Programming in the Browser
How WebGPU compute shaders unlock general-purpose GPU programming in the browser: WGSL pipelines, workgroups, storage buffers, and real-world physics/ML use cases.
ArticleElectronics
Op-Amps: The Virtual Short and Essential Circuits
The operational amplifier is analog electronics' key building block — analyze inverting amps, integrators, filters, and comparators.
ArticleMachine Learning
Neural Network Backpropagation — How Training Actually Works
How neural networks learn via backpropagation: forward pass, loss computation, chain rule gradients, weight updates, and the intuition behind why it works.
ArticleMachine Learning
Build a Neural Network from Scratch in JavaScript
Implement a fully-connected neural network from scratch in JavaScript: matrix multiply, activations, forward pass, backpropagation, SGD — zero dependencies.
ArticleMachine Learning
Neural Networks & Backpropagation — The Maths Behind AI
From perceptron to deep learning: forward pass, cross-entropy loss, backpropagation via chain rule, SGD, vanishing gradients, ReLU, and batch normalisation.
ArticleTheoretical Physics
String Theory Basics
An introduction to string theory — 1D strings, extra dimensions, supersymmetry, M-theory, D-branes, the landscape problem, and AdS/CFT holography.
ArticleCondensed Matter Physics
Superconductivity: Zero Resistance and the Meissner Effect Explained
Cooper pairs, BCS theory, the Meissner effect, Type I vs Type II superconductors, high-temperature cuprates, and applications in MRI and maglev.
ArticleEvolutionary Computation
Evolutionary Algorithms — Natural Selection as Computation
Genetic algorithms, NEAT, CMA-ES: how evolutionary algorithms harness selection, crossover, and mutation to solve problems no gradient can reach.
ArticlePhysics
Magnetism Explained: From Atoms to Hard Drives
Understanding magnetism — diamagnetism, paramagnetism, ferromagnetism, exchange interaction, magnetic domains, hysteresis, and technology applications.

🔍 How Things Work

11 articles
ArticleClassical Mechanics
How Does a Lever Work? Force, Fulcrum and Arm
A lever lets you lift heavy objects with less force. Learn the three parts of a lever, Archimedes' famous quote, and everyday examples.
ArticleApplied Physics
How a Microwave Oven Works — The Physics of Heating Water
Why does a microwave heat food in seconds? The dipole moment of water molecules, dielectric heating at 2.45 GHz, and standing waves inside the cavity.
ArticleOptics
How Does a Rainbow Work? — Refraction, Reflection & Dispersion
How a rainbow forms: refraction and total internal reflection inside raindrops, dispersion of white light, and why colours always appear in the same order.
ArticleThermal Physics
How a Thermos Works — Three Ways Heat Travels
A thermos keeps drinks hot or cold by blocking all three forms of heat transfer: conduction, convection, and radiation. Here is the physics of each.
ArticleAerodynamics
Boomerang Physics: Why It Comes Back
Gyroscopic precession, differential lift, and spin stabilisation — the aerodynamics that make a flat piece of wood fly in a circle and return.
ArticleThermodynamics
How Refrigerators Work: The Thermodynamics of Cooling
Refrigerator physics explained — vapour-compression cycle, phase changes, COP, refrigerants, heat pumps, and the second law of thermodynamics.
ArticleAerodynamics
Why a Boomerang Returns — Gyroscopic Precession Explained
A boomerang returns because its two spinning wings generate unequal lift, and gyroscopic precession curves that torque into a circular path home.
ArticleOptics
Why Is the Sky Blue? Rayleigh Scattering Explained
Why the sky is blue and sunsets are red — Rayleigh scattering, light wavelength physics and the atmosphere, explained for all ages.
ArticleEveryday Physics
How Microwave Ovens Work: From Magnetron to Hot Food
The physics of microwave ovens — magnetrons, dielectric heating, standing waves, why plates rotate, and why metal sparks.
ArticleClassical Mechanics
Pendulum & Newton's Cradle — Conservation of Momentum for Kids
Why does exactly one ball fly out of Newton's Cradle? Discover conservation of momentum and energy with pendulums, explained for kids aged 8-14.
ArticleAerospace Physics
How Does a Rocket Work? Newton's Third Law for Kids
Discover how rockets fly using Newton's Third Law, why they carry so much fuel, and how staging makes space travel possible — explained simply for kids.

🎓 Tutorials

64 tutorials
01
Your First Simulation in 30 Minutes
Three.js from scratch: renderer, scene, camera. Five steps to moving particles.
⏱ 30 minBeginner
02
Three.js for Beginners
Geometries, materials, lighting, textures, OrbitControls — all the basics.
⏱ 45 minBeginner
03
GLSL Shaders from Scratch
Vertex and fragment shaders, uniforms, varyings, passing data to the GPU.
⏱ 60 minIntermediate
04
Cannon-es: Physics Bodies and Collisions
World, Body, Shape. Syncing Three.js + Cannon-es. RaycastVehicle.
⏱ 50 minIntermediate
05
Optimising Simulations: InstancedMesh and Spatial Hashing
From 500 to 50,000 particles at 60fps. InstancedMesh, WebWorker, spatial hashing.
⏱ 40 minAdvanced
06
Fluid Simulation in an Evening
SPH implementation from scratch. Spatial partitioning, kernels, integration. Full code.
⏱ 90 minAdvanced
07
How to Build Your Own Simulation
Template from idea to publication. File structure, HUD, controls hint, responsive.
⏱ 35 minBeginner
08
Pathfinding Algorithm Visualiser
A*, Dijkstra, BFS in live animation on Canvas 2D. Maze + interactive walls.
⏱ 70 minIntermediate
09
Solar System in Three.js
Textured planets, Keplerian orbits, CSS2D labels, speed slider, UnrealBloom post-processing.
⏱ 60 minIntermediate
10
GLSL Fire & Water Shader
fBm noise fire with colour ramp, Gerstner waves, Fresnel caustics — raw WebGL2 & Three.js ShaderMaterial.
⏱ 55 minAdvanced
11
Save Settings with localStorage
Persist slider values, toggles and camera state across reloads with JSON, schema versioning and IndexedDB.
⏱ 35 minBeginner
12
Path Tracing in WebGL (GLSL): A Real-Time Ray Tracer From Scratch
Build a real-time path tracer in WebGL2 and GLSL: rendering equation, Monte Carlo integration, cosine-weighted hemisphere sampling, progressive…
⏱ 75 minAdvanced
13
Procedural Textures: Theory to Shader
From value noise to Worley cells: build procedural textures from first principles and implement them as GLSL fragment shaders — noise functions, FBM…
⏱ 50 minIntermediate
14
Post-Processing Effects in Three.js: EffectComposer, Bloom & SSAO
Complete guide to Three.js post-processing with EffectComposer — RenderPass, UnrealBloomPass, SSAOPass, FXAA/SMAA, film grain, and a custom GLSL…
⏱ 45 minIntermediate
15
Particle Simulator with Springs (PBD)
Build a Position Based Dynamics (PBD) particle simulator with spring/distance constraints in JavaScript: Verlet integration, constraint projection…
⏱ 55 minIntermediate
16
N-Body Barnes-Hut Algorithm from Scratch — Tutorial
Implement the Barnes-Hut octree N-body algorithm from scratch in JavaScript: tree construction, multipole approximation theta criterion, force…
⏱ 60 minAdvanced
17
Rigid Body Physics: SAT and EPA Collision Detection
Deep dive into rigid body collision detection: the Separating Axis Theorem (SAT) for convex polytopes, GJK for distance queries, and the Expanding…
⏱ 70 minAdvanced
18
Procedural Terrain Generation with Erosion Simulation
Generate realistic 3D terrain from scratch: layered Simplex noise heightfields, domain warping, droplet-based hydraulic erosion, thermal erosion, and…
⏱ 65 minIntermediate
19
L-Systems: From String to 3D Plant
Learn how Lindenmayer systems (L-systems) turn a short rewriting grammar into realistic 3D trees and plants: production rules, turtle interpretation…
⏱ 45 minIntermediate
20
Introduction to WebGPU: First Steps
Get started with WebGPU: adapters, devices, GPUBuffer, WGSL shaders, render pipelines, and compute passes. A hands-on tutorial for the successor to…
⏱ 40 minBeginner
21
Compute Shaders: Massively Parallel Simulation
Learn WebGPU compute shaders from first principles: workgroups, storage buffers, dispatch, and a full WGSL particle simulation running hundreds of…
⏱ 60 minAdvanced
22
Rust + WebAssembly for Simulations
Compile a particle physics simulation written in Rust to WebAssembly and render 100k particles at 60fps in the browser.
⏱ 35 minIntermediate
23
Offline-First App with Service Workers
Make your simulation work offline: cache-first strategy, background sync, Workbox vs vanilla SW, and Web App Manifest for installability.
⏱ 35 minIntermediate
24
Spatial Hashing for O(1) Neighbour Lookup
Build a uniform spatial hash grid in JavaScript for O(1) average neighbour queries in particle systems, collision detection, and SPH fluid.
⏱ 35 minIntermediate
25
SPH Fluid Simulation from Scratch in 200 Lines
Implement a 2D Smoothed Particle Hydrodynamics fluid simulation from scratch in 200 lines of JavaScript using Poly6, Spiky, and Viscosity kernels.
⏱ 50 minAdvanced
26
Three.js Performance Optimization — InstancedMesh, LOD, Web Workers
Render 100,000+ objects at 60fps with InstancedMesh, frustum culling, LOD, BufferGeometry, Web Workers for physics, and GPU picking.
⏱ 50 minAdvanced
27
Three.js Shadows — PCF, VSM, CSM & Tuning
Master shadow rendering in Three.js: shadow map types (PCF, PCFSOFT, VSM), cascaded shadow maps, bias tuning, and performance best practices.
⏱ 35 minIntermediate
28
WebGL Transform Feedback — GPU Particle Systems
Use WebGL Transform Feedback to update particle positions entirely on the GPU, eliminating CPU readback for millions of particles in real time.
⏱ 50 minAdvanced
29
3D Voronoi & Delaunay in the Browser
Generate Voronoi diagrams and Delaunay triangulations in the browser using Fortune's algorithm, then lift them into 3D with Three.js.
⏱ 35 minIntermediate
30
Build a 3D Voxel Engine in WebGL
Build a Minecraft-style voxel engine in the browser: chunk-based world, greedy meshing, face culling, and smooth or blocky terrain rendering.
⏱ 35 minIntermediate
31
WebGL Transform Feedback — GPU Particle Simulation Tutorial
Build a GPU particle simulation with WebGL2 Transform Feedback: ping-pong VAO pattern, GLSL updates, 1M particles at 60fps with no CPU involvement.
⏱ 50 minAdvanced
32
Neural Network from Scratch in Vanilla JS
Build a fully-connected neural network from scratch in JavaScript: forward pass, backpropagation, SGD, and training on XOR and sine approximation.
⏱ 50 minAdvanced
33
Numerical Integration for Physics — Euler, Verlet & RK4
Compare Euler, symplectic Euler, Verlet, and Runge-Kutta 4 integration methods for physics simulations, with energy stability analysis and a spring-mass demo.
⏱ 35 minIntermediate
34
Offscreen Canvas + Web Workers
Move Three.js and WebGL rendering off the main thread with OffscreenCanvas and a dedicated Web Worker, keeping the UI responsive at all times.
⏱ 35 minIntermediate
35
Particle System with LOD and Billboards
Build a high-performance particle system in Three.js using BufferGeometry, billboard particles, and level-of-detail switching for 100k+ particles.
⏱ 35 minIntermediate
36
PID Controller: Theory and Tuning
A complete guide to PID controllers: proportional, integral, and derivative terms, discrete-time implementation, anti-windup, derivative kick, and Ziegler-Nichols tuning.
⏱ 20 minBeginner
37
Procedural Music with Web Audio API
Generate algorithmic music in the browser using Web Audio API oscillators, sequencers, chord progressions, and basic synthesis patches.
⏱ 35 minIntermediate
38
Procedural Terrain with Hydraulic Erosion in Three.js
Build a procedurally generated 3D terrain using Perlin noise and simulate hydraulic erosion to carve realistic valleys, rivers, and ridges.
⏱ 35 minIntermediate
39
Procedural Terrain Generation
Generate infinite 3D terrain in Three.js using layered Perlin noise (fBm), heightmap vertex displacement, normal recalculation and colour grading.
⏱ 35 minIntermediate
40
Quaternions — Rotation Without Gimbal Lock
Master quaternions for 3D rotation: Hamilton product, Euler conversion, slerp interpolation, gimbal lock explanation, and the Three.js Quaternion API.
⏱ 35 minIntermediate
41
RenderTarget & Post-processing in Three.js
Use Three.js WebGLRenderTarget to implement bloom, depth of field, chromatic aberration, and custom post-processing passes without libraries.
⏱ 35 minIntermediate
42
GLSL Fire Shader Effect
Build a procedural fire shader in GLSL: layered Perlin noise, colour palettes, UV distortion, and animated billboarding in Three.js.
⏱ 35 minIntermediate
43
GPU Game of Life in 50 Lines of GLSL
Run Conway's Game of Life entirely on the GPU using WebGL ping-pong render targets and a 50-line GLSL fragment shader.
⏱ 50 minAdvanced
44
GPU-Accelerated L-System Trees
Generate realistic 3D trees and fractals using L-systems, then render 100,000+ branches at 60 FPS with GPU instancing in Three.js.
⏱ 50 minAdvanced
45
Gray-Scott Reaction-Diffusion on GPU with WebGL
Implement the Gray-Scott reaction-diffusion system in WebGL 2 using ping-pong framebuffers and a fragment shader, running at 60 fps.
⏱ 50 minAdvanced
46
InstancedMesh Guide: 1,000,000 Objects at 60 FPS
Three.js InstancedMesh tutorial — setMatrixAt, per-instance colour, GPU picking, manual frustum culling, and rendering 1M particles at 60 FPS.
⏱ 50 minAdvanced
47
Lattice-Boltzmann Fluid in 200 Lines
Implement the D2Q9 Lattice-Boltzmann Method fluid simulation in 200 lines of JavaScript: streaming, collision, bounce-back, colour rendering.
⏱ 35 minIntermediate
48
Lattice Boltzmann Fluid Simulation
Implement a 2D D2Q9 Lattice Boltzmann Method fluid simulation in JavaScript, rendered in real-time with a canvas velocity colour map.
⏱ 50 minAdvanced
49
Lattice Boltzmann Fluid Simulation in WebGL
Implement a 2D D2Q9 Lattice Boltzmann fluid simulation entirely on the GPU using WebGL textures, ping-pong rendering, and fragment shaders.
⏱ 50 minAdvanced
50
Terrain with Marching Cubes & Perlin Noise
Generate smooth isosurface terrain using the Marching Cubes algorithm and 3D Perlin noise, rendered in Three.js with normals and lighting.
⏱ 50 minAdvanced
51
Markov Chain Text Generator
Build a Markov chain text generator in JavaScript — n-gram model, training on any corpus, temperature sampling, and coherent-sounding sentences.
⏱ 35 minIntermediate
52
WebAudio API Spectrum Visualizer
Build a real-time audio spectrum visualizer with the Web Audio API — FFT analysis, bar chart, waveform oscilloscope, and Three.js 3D bars.
⏱ 35 minIntermediate
53
Behavior Trees: AI for NPCs
Build a behavior tree engine from scratch in vanilla JavaScript: composite nodes, decorators, blackboards, and a working guard NPC.
⏱ 50 minAdvanced
54
Build a Physics Engine From Scratch in JavaScript
Build a rigid-body physics engine from scratch in JavaScript: AABB broad phase, SAT narrow phase, impulse-based collision response, angular dynamics, and constraint solving.
⏱ 50 minAdvanced
55
Custom ShaderMaterial in Three.js
Write a fully custom GLSL vertex and fragment shader in Three.js using ShaderMaterial — uniforms, varyings, texture sampling, and noise-driven effects.
⏱ 35 minIntermediate
56
Debugging WebGL — DevTools, Spector.js & Profiling
Learn to debug WebGL and Three.js applications: browser GPU timeline, WEBGL_debug_renderer_info, Spector.js frame capture, error checking, and draw call reduction.
⏱ 50 minAdvanced
57
Drone Swarm Simulation — Flocking + Formation Control Tutorial
Build a drone swarm simulation with Boids flocking, V-formation, circle and grid formations, leader-follower, and obstacle avoidance using JavaScript and Three.js.
⏱ 35 minIntermediate
58
ECS Architecture for Large-Scale Simulations in JavaScript
Build a cache-friendly Entity-Component-System (ECS) in JavaScript for particle and physics simulations, with Structure of Arrays layout and benchmarks.
⏱ 50 minAdvanced
59
Procedural Animation with FABRIK Inverse Kinematics
Implement FABRIK (Forward And Backward Reaching IK) for procedural animation in JavaScript — spider legs, robotic arms, and tentacle motion with a canvas demo.
⏱ 35 minIntermediate
60
Generative Art with p5.js and GLSL Shaders Tutorial
Create generative art using p5.js for creative coding and GLSL fragment shaders for GPU-rendered visuals — flow fields, Perlin noise, and Truchet tiles.
⏱ 50 minAdvanced
61
Genetic Algorithm — Solve the TSP
Build a genetic algorithm to approximate the Travelling Salesman Problem: population init, ordered crossover, swap mutation, tournament selection, and fitness animation.
⏱ 35 minIntermediate
62
WebSocket Real-Time Simulation Sync — Tutorial
Sync a browser physics simulation in real time via WebSocket — heartbeat, reconnection, delta compression, and room-based multiplayer.
⏱ 35 minIntermediate
63
AR in Browsers: Plane Detection & Hit Testing
Use WebXR hit-testing and plane detection to place 3D objects on real surfaces in mobile AR — no app install required.
⏱ 35 minIntermediate
64
WebXR Device API — First Steps
Enter VR and AR from the browser using the WebXR Device API — set up an XR session, handle controller input, and render a stereo 3D scene.
⏱ 35 minIntermediate

📚 References

29 references
🔧
WebGL Cheatsheet
API, states, extensions
GLSL Cheatsheet
Functions, types, precisions
📐
Mathematical Formulae
Vectors, matrices, quaternions
⚛️
Physical Constants
G, c, kB, h, NA
📖
Algorithm Glossary
SPH, BVH, ACO, RK4…
🔢
Numerical Methods
ODE integration, PDE
📊
Algorithm Complexity
Big-O table for simulations
⚖️
Simulation Comparison
Cost, accuracy, approach
⚖️
Comparison of Simulation Methods — Euler, Verlet, RK4, SPH & More
Euler, Verlet, RK4, SPH
🔢
Numerical Methods Cheatsheet · 3D Simulations
ODE, roots, FFT
🧩
Three.js API Quick Reference · 3D Simulations
Scene, camera, materials
🖥️
WGSL Cheatsheet — 3D Simulations
WebGPU shader syntax
🎨
Color Spaces Reference · 3D Simulations
sRGB, HSL, CIELAB
🌐
i18n Guide for the Project
EN/UK site structure
📄
New Simulation Template — Contributor Reference
New sim boilerplate
Simulation Launch Checklist — Contributor Reference
Pre-launch QA checklist
📄
Physics Simulation Learning Resources — Books, Courses, Papers, Datasets
Curated books, YouTube channels, research papers, datasets a
📐
3D Matrix Cheat Sheet — Model, View, Projection
All the 4×4 matrices you need for 3D graphics: translation,
⚛️
JavaScript Physics Engines Comparison — Cannon-es vs Rapier vs Ammo.js
Comprehensive comparison of browser physics engines: Cannon
📄
Landmark Simulation Papers and Open-Source References
Curated list of foundational simulation papers: SPH, LBM, PB
🎨
Three.js Design Patterns & Best Practices
Three
🎨
Three.js r160 Changelog & Migration Guide
Three
🔊
Web Audio API Cheatsheet — AudioContext, Nodes & DSP
Complete Web Audio API reference: AudioContext graph, Oscill
🔧
WebGL Extension Reference
Complete reference for WebGL 1 and WebGL 2 extensions: OES_t
🔧
WebGL 1 & 2 Specification Reference
Comprehensive WebGL 1 and WebGL 2 API reference: context, sh
📐
Calculus for Simulations: Cheat Sheet
Vector calculus, PDE classification, finite difference schem
⚛️
CFD Glossary — Dimensionless Numbers, Flow States & Boundary Conditions
Comprehensive CFD reference covering dimensionless numbers (
⚛️
Equations of Motion Reference
Common physics equations of motion for simulations: kinemati
📐
Floating-Point Traps in Simulation Code — Reference
IEEE 754 format, NaN/Infinity, catastrophic cancellation, ep
⚛️
Game Physics Formulas — Cheat Sheet
Complete game physics formulas: impulse
🎨
Generative Art Algorithms Reference
Perlin noise, simplex noise, Voronoi, L
🔧
GLSL Built-in Functions Quick Reference
Complete GLSL ES 3
🔍

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