📐 Mathematics

Parametric Spirograph PatternsExplore intricate spirograph patterns by adjusting the radii of two concentric circles and… Fractal ExplorerPopularMandelbrot and Julia sets rendered with smooth-colouring GLSL shaders. Pan, zoom, switch… Number SpiralsUlam spiral (prime diagonals), Sacks spiral, Fibonacci sunflower and composite highlight… Geodesic DomesInteractive 3D geodesic dome builder. Subdivide icosahedra, octahedra and tetrahedra at… Spherical ProjectionsCompare Mercator, Mollweide, Lambert azimuthal equal-area, sinusoidal and equirectangular… Sierpiński TriangleTwo methods: Chaos Game (random vertex jumps) and recursive subdivision. Hausdorff dimension… 1D Cellular Automata — WolframExplore all 256 Wolfram elementary cellular automaton rules. Watch Rule 30, 90, 110 and 184… Kaleidoscope: Infinite Symmetry ArtExplore the mesmerizing world of infinite symmetry by manipulating folding parameters and… Pythagoras TreeA recursive fractal tree built from the Pythagorean theorem. Adjust branch angle, depth and… Voronoi DiagramInteractive Voronoi tessellation with Lloyd's algorithm for centroidal relaxation. Choose… Chaotic Fern Iteration SystemExplore the mesmerizing growth of a Barnsley fern through an iterative function system,… Taylor Series — Polynomial ApproximationNewVisualise how Maclaurin polynomials approximate sin(x), cos(x) and eˣ. Slide N from 1 to 20… The 3n+1 Rule: Exploring the Collatz ConjectureObserve the iterative process of the 3n+1 rule as you input a starting number and watch its… Volcano Eruption: A Riemann Integral SimulationWitness the dramatic buildup and explosive release of a volcano, modeled using the… Möbius Strip — Topology One-Sided SurfaceTrace a path along a Mobius strip to prove it has one side and one edge, then cut it… Matrix Transformations — 2D Linear Algebra VisualizerType a 2x2 matrix and watch the plane rotate, shear or scale, with the determinant as area… Klein Bottle — Topology of Non-Orientable SurfacesRotate an immersed Klein bottle, follow its self-intersection, and see how two Mobius strips… Torus & Surface Genus — Topology of Orientable SurfacesCompare a sphere, torus and double torus by genus and Euler characteristic, and see how a… Knot Theory — Invariants, Crossings & Reidemeister MovesDeform a trefoil or figure-eight knot with Reidemeister moves and watch crossing number,… Eigenvalues & EigenvectorsInteractive 2D matrix visualizer: watch the unit circle transform into an ellipse,… SVD VisualizerWatch a 2x2 matrix decompose as A=UΣVᵀ: rotate, stretch by singular values, then rotate… Fourier Series DecompositionExplore the breakdown of complex waveforms into simpler sinusoidal components using the… Wind Farm: A Riemann Integral SimulationObserve how kinetic energy is converted into electricity by a wind farm, visualized through… Fourier Series — Interactive Phasor & Harmonic Decomposition SimulatorBuild waveforms from sine harmonics interactively. Watch rotating phasors trace square,… Sieve of Eratosthenes — Animated Prime Number FinderWatch the Sieve of Eratosthenes animate in real time. Cross off multiples of each prime and… Eigenvectors & Eigenvalues — Interactive Linear Algebra VisualizerAdjust 4 matrix entries and instantly see characteristic polynomial, eigenvalues λ₁ λ₂,… Torus & Genus — Topology Euler Characteristic InteractiveGenus 0–3 surfaces (sphere, torus, double-torus, triple-torus). χ = V−E+F. Gauss-Bonnet… Newton's FractalNewton's method applied to z^n − 1 = 0 in the complex plane. Each pixel is coloured by which… Sand Pile ModelBak–Tang–Wiesenfeld self-organised criticality. Drop grains of sand onto a grid; cells with… Complex FunctionsDomain coloring of complex functions. Hue encodes the argument and brightness encodes the… Diffusion-Limited Aggregation Fractal GrowthObserve how particles spontaneously clump together in a fractal pattern as they randomly… Phase PortraitTune the parameters of a 2D dynamical system and watch trajectories in the vector field… Reaction-Diffusion Patterns in a Turing SystemExplore how patterns emerge and evolve within a reaction-diffusion system by adjusting feed… Harmonograph: Pendulum Wave PatternsNewExplore how two swinging pendulums create mesmerizing, repeating patterns by adjusting their… SVD CompressionNewKeep only the top k singular values of an image and watch how few rank-1 layers are needed… Bézier CurvesNewDrag control points and step the de Casteljau construction to see how a Bezier curve is… Brouwer Fixed Point TheoremNewStir and squash a disc onto itself and see why at least one point always stays put, the… Derivative VisualizerNewSlide the point x0 and shrink the step h to watch a secant line collapse onto the tangent,… DFT & STFT VisualiserGenerate signals and watch their Fourier transforms live. Switch between DFT magnitude… Eigenvalues & Eigenvectors — Linear Transformation VisualiserNewInteractive 2×2 matrix transformation visualiser. Drag matrix entries to see how… Space-Filling CurvesNewWatch Hilbert, Peano and Morton (Z-order) curves fill the plane. Colour by path position to… Ulam SpiralNewLay the integers on a square spiral and mark the primes — striking diagonal patterns emerge.… Fourier Epicycles: Rotating Circle ChainsNewExplore the relationship between geometric shapes and oscillating waves as you draw a closed… Mandelbulb 3D FractalNewExplore the mesmerizing geometry of the Mandelbrot set and its associated fractal – the… Origami Fold MathematicsNewExplore the mathematics of paper folding — crease patterns, fold sequences and rigid origami… Hypocycloids & Epicycloids — Rolling Circle CurvesNewWatch a circle roll inside or outside a fixed circle and trace roulette curves — deltoid,… Newton's Method Fractal — Basins of AttractionNewEach pixel iterates Newton's method in ℂ toward a root, colored by which root it reaches.… Rose Curves — Rhodonea r = a·cos(kθ)NewDraw rose curves r = a·cos(kθ) in polar coordinates. Set k = n/d, watch the parity rule… 3D Lissajous Curves — Harmonic KnotsNewThree perpendicular oscillators woven into a 3D Lissajous curve. Tune frequencies a:b:c and… Riemann Zeta Function — Critical Strip & ZerosNewVisualise the Riemann zeta function on the complex plane: domain-colour ζ(s), walk the… Continued Fractions — Best Rational ApproximationsNewUnfold any real number into continued fraction [a0; a1, a2,…] and watch convergents p/q… Spirograph — Hypotrochoids & EpitrochoidsNewDraw parametric rolling-circle curves: hypotrochoids trace inside a fixed ring, epitrochoids… Penrose Tiling — Quasi-Periodic PatternsNewGenerate Penrose P3 (thick and thin rhombus) tilings via deflation substitution. These… Eigenvalues — Linear Transformations & Principal AxesNewEdit a 2x2 matrix and watch it transform the unit circle into an ellipse: eigenvectors point… Soap Bubble — Minimal Surface SimulationNewSimulate soap films finding minimal surfaces. Plateau relaxation minimizes surface area.… 3D Cellular Automaton — Survival/Birth RulesNewExplore 3D cellular automata with Moore neighborhood (26 neighbors). Famous rules: Cloud,… Hyperbolic Geometry TilingNewTessellate the Poincaré disk model of hyperbolic plane with {p,q} regular tilings. Möbius… p-adic Number Ultrametric SpaceNewVisualize p-adic numbers as a fractal tree. The p-adic distance |x-y|_p = p^{-v_p(x-y)}… Prime Distribution & GapsNewVisualize prime number distribution: spiral (Ulam), prime gaps histogram, and the Prime… Weierstrass Nowhere-Differentiable FunctionNewThe Weierstrass function W(x) = Σ aⁿ·cos(bⁿπx) is continuous everywhere but differentiable… Buffon's NeedleNewDrop random needles onto a floor ruled with parallel lines and watch pi emerge from the… Dragon CurveNewGenerate the Heighway dragon curve from its recursive L/R turn-sequence doubling rule and… Fibonacci Spiral — Golden Ratio VisualizerNewExplore the Fibonacci spiral, the golden angle, and the golden ratio φ≈1.618034 with an… Ford Circles & Farey SequenceNewEvery reduced fraction p/q between 0 and 1 has a Ford circle tangent to the number line at… Koch SnowflakeNewBuild the Koch snowflake by recursively replacing the middle third of every segment with an… Monte Carlo Pi EstimationNewEstimate the value of pi by scattering random points into a square and counting how many… Pascal's Triangle mod pNewCompute binomial coefficients C(n,k) modulo a small prime and colour each cell by its… Peano Space-Filling CurveNewWatch Giuseppe Peano's 1890 space-filling curve unfold through a recursive 3x3 boustrophedon… Platonic SolidsNewInteractive Platonic solids explorer. Rotate wireframe or solid-shaded tetrahedra, cubes,… Recamán's Sequence VisualizationNewObserve Recamán's Sequence develop dynamically, with arcs representing each term, and adjust… Sierpinski CarpetNewRecursively subdivide a square into a 3x3 grid, removing the center square at every level,… Wallpaper Symmetry GroupsNewNine of the 17 mathematically possible wallpaper groups, built by tiling an asymmetric motif… The Derivative as a LimitNewInteractive 3D curve where dragging a secant line's second point closer to a fixed point… Eigenvalues and Eigenvectors: The Directions a Matrix Refuses to RotateNewInteractive 3D vector field where adjusting a transformation matrix's entries shows most… Prime Distribution and GapsNewInteractive 3D number-line visualization where scrubbing through increasing ranges of… Wallpaper Symmetry Group ExplorerNewInteractive 3D tiled plane where switching among the 17 wallpaper groups shows how rotation,… Voronoi & Lloyd's Relaxation ExplorerNewInteractive 3D point set where running Lloyd's relaxation iterations shows how Voronoi cells… Riemann Zeta Critical Strip ExplorerNewInteractive 3D complex plane where sweeping through the critical strip shows how the Riemann… Complex Function VisualizerNewThis simulation demonstrates how to visualize complex mathematical functions by coloring… ML Model Training: Apartment Price PredictionNewExplore how different training parameters – learning rates, epochs, and feature selection –… Cyclic Group Zn — Cayley GraphNewVisualize the cyclic group Zn as points on a ring: pick a generator g and watch the Cayley… Elliptic Curve y² = x³+ax+b — Group Law & Bézout's TheoremNewInteractive algebraic geometry: the Weierstrass cubic y² = x³+ax+b, a secant/tangent line… Algebraic Topology: Genus, Handles & Homology ExplorerNewBuild a genus-g handlebody by attaching handles to a sphere and watch its homology… Algebraic Number Theory: Rings, Ideals and Number FieldsNewExplore the fundamental concepts of algebraic number theory through an interactive… Loss Landscape OptimizerNewExplore advanced mathematical topics in hyperparameter optimization. Learn about… Analytic Number Theory: Prime Spiral & the Prime-Counting FunctionNewWatch a rising Sacks-style spiral of the integers light up with prime numbers. Sweep the… Linear Algebra SimulatorNewWatch a 2x2 matrix transform a live vector grid in real time: see basis vectors,… Multi-Objective Optimization MathematicsNewExplore multi-objective optimization mathematics. Learn about Pareto optimality, Pareto… Search Space Analysis: Mathematics of Hyperparameter SpacesNewLearn about search space analysis in hyperparameter optimization. Understand dimensionality,… The Life-Cycle Math of ClothingNewAn interactive 3D pipeline that turns fiber choice, dyeing intensity, shipping mode and… Spirograph - Hypotrochoid Pattern GeneratorNewThis simulation illustrates the creation of intricate patterns using a spirograph,… Sunflower Field - Phyllotaxis PatternNewThis simulation explores phyllotaxis, the arrangement of leaves around a stem in plants like… Impossible TriangleNewThis simulation demonstrates the principles of Euclidean geometry and how it's impossible to… Thermal Fracture of a Voronoi RegionNewExplore the dynamic breakdown of a Voronoi diagram as it undergoes thermal stress,… Möbius Ant WalkNewThis simulation explores the unique properties of a Möbius strip by visualizing an ant… Origami Crane Fold: Origami FoldingNewOrigami Crane Fold - this variant focuses on origami folding. Abacus CalculationNewThis simulation demonstrates the operation of an abacus as a tool for performing arithmetic… Spirograph Gear DrawingNewThis simulation visually demonstrates the mathematical relationships behind spirograph… Recursive Fractal Tree SimulationNewWitness a visually captivating fractal tree evolve through mathematical recursion. Adjust… Fractal Branching DynamicsNewObserve the generation of complex fractal patterns via recursive branching, showcasing how… Mandelbrot ShaderNewThis simulation generates a Mandelbrot set using a shader. It demonstrates the iterative… Kaleidoscope Geometric PatternsNewThis simulation visualizes the patterns generated by a kaleidoscope. It demonstrates how… Three-Dimensional Kaleidoscope PatternsNewExplore the captivating visual effects generated by a rotating, geometric kaleidoscope… 3D Armillary SphereNewThis simulation demonstrates the armillary sphere, a historical instrument used for… 3D Fractal ExplorerNewThis interactive simulation explores the generation and visualization of fractals within a… 3D Fractal TreeNewThis simulation visually represents the generation of fractal patterns using recursive… 3D Galton BoardNewThis simulation allows you to explore the distribution of random outcomes produced by a… 3D Galton Board OskNewThis simulation demonstrates the probabilistic nature of random walks and the distribution… 3D HarmonographNewA visual representation of complex mathematical functions through the movement of… 3D Knot TheoryNewThis simulation explores the visual representation of knots in a three-dimensional space. It… 3D Lsystem Plant GrowthNewThis simulation demonstrates the growth of plants using L-systems. Users can manipulate… 3D MandelbulbNewWitness the mesmerizing beauty of a Mandelbulb, a fractal shape generated by complex… 3D Menger SpongeNewThis simulation demonstrates the growth of a Menger sponge in three dimensions. It allows… 3D Pascals TriangleNewThis simulation visually represents Pascal’s triangle, showcasing the relationships between… 3D Platonic Solids DualityNewThis simulation demonstrates the geometric relationships between platonic solids and their… 3D Prime Number SpiralNewThis simulation generates a spiral pattern using prime numbers, visually representing the… Complex Origami Folding PatternsNewThis simulation lets you explore intricate origami designs by manipulating virtual paper and… Mandelbulb Fractal: Mandelbrot SetNewMandelbulb Fractal - this variant focuses on mandelbrot set. Mandelbulb Fractal: ZoomNewMandelbulb Fractal - this variant focuses on zoom. Harmonograph: Rotating Cam SimulationNewWitness the creation of complex geometric patterns through a rotating cam mechanism,… Mandelbulb Fractal: Complex GeometryNewMandelbulb Fractal - this variant focuses on complex geometry. Lissajous Sand Pendulum / HarmonographNewThis simulation recreates the mesmerizing patterns produced by a Lissajous sand pendulum. It… Procedural SnowflakesNewThis simulation demonstrates the generation of complex snowflake patterns using procedural… 3D Cellular Automaton: 3d DynamicsNew3D Cellular Automaton - this variant focuses on 3d dynamics. 3D Voronoi GrowthNewThis simulation illustrates the concept of Voronoi diagrams and their growth patterns. Users… Sunflower PhyllotaxisNewThis simulation explores the mathematical patterns governing the arrangement of sunflower… Nanotechnology in Crystal StructuresNewThis simulation explores how manipulating nanomaterials within a crystalline structure… Advanced Mathematics - Comprehensive GuideNewThis simulation demonstrates fundamental mathematical concepts through interactive… Boolean Algebra Explained — Logic, Gates, and SimplificationNewThis simulation visually teaches the principles of Boolean algebra through interactive logic… Calculus Visualizer Derivatives IntegralsNewThis interactive visualization allows you to explore the core concepts of calculus –… Cellular Automata Explained — Local Rules, Global PatternsNewThis simulation illustrates the fascinating behavior of cellular automata. Users can… Chain PolymerizationNewThis simulation demonstrates the process of chain polymerization, where small monomers… Chemistry-Computational-Chemistry-LabNewThis simulator combines computational tools with a laboratory environment for exploring… Chromite Spiral SeparatorNewThis simulation visualizes the complex geometry and flow patterns within a chromite spiral… Clifford AttractorNewThis simulation explores the Clifford attractor, a complex mathematical system that… Collatz Conjecture: Iterative Number SequencesNewVisually trace the progression of a number through the Collatz conjecture, observing how it… Combinatorics Explained — Counting, Permutations, and GraphsNewThis simulation demonstrates the fundamental concepts of combinatorics, including counting… Computational Mathematics - Comprehensive GuideNewThis simulation demonstrates computational mathematics by showcasing numerical methods for… Correlation MatrixNewThis simulation visualizes a correlation matrix, illustrating how different variables relate… Correlation Matrix Heatmap - Interactive Data AnalysisNewThis simulation provides an interactive visualization of a correlation matrix, allowing… Data Distribution Explorer - Statistical VisualizationNewThis simulation displays a visualization of a data distribution, offering insights into the… Data Distribution Explorer - Statistical Visualization ToolNewThis simulation allows users to visualize the distribution of a dataset using various… Data Structures Explained — Arrays, Trees, Graphs, and HeapsNewThis simulation provides an interactive visual explanation of fundamental data structures.… Delaunay MeshNewThis simulation demonstrates the Delaunay triangulation algorithm, which creates a mesh of… Differential Equations Phase Portraits AnalysisNewThis simulation allows you to explore complex systems by visualizing their solutions as… Differential Geometry Explained — Curves, Surfaces, and CurvatureNewThis interactive simulation provides a visual introduction to differential geometry… Fourier Epicycles: A Visual ExplorationNewThis simulation visually demonstrates the concept of epicycles, showcasing how ancient… Mandelbrot Set ExplorationNewExplore the mesmerizing world of fractal geometry! This simulation demonstrates how… Fractal Geometry Exploration SimulationNewExplore the fascinating world of fractal geometry by manipulating iteration depth and… Fractal Tree GenerationNewExplore the creation of intricate, self-similar tree structures using recursive algorithms… Fractals Explained: Self-Similarity and the Mandelbrot SetNewExplore the mesmerizing world of fractals with this simulation! Witness how the Mandelbrot… Galton Board SimulationNewObserve balls cascading through a peg board, demonstrating the binomial distribution and its… Gem Faceting SimulationNewThis simulation allows users to explore the process of gem faceting, demonstrating how light… Geological Block ModelNewThis simulation allows users to visualize and interact with a geological block model – a… Geometallurgical Block Model SimulationNewThis simulation demonstrates the creation and application of a geometallurgical block model.… Gradient Descent Simulator - Optimization VisualizerNewThis simulator visualizes the process of gradient descent optimization, allowing users to… Gradient Descent VisualizationNewThis simulation visually represents the gradient descent optimization algorithm,… Harmonograph Lissajous CurvesNewAn interactive 2D simulation demonstrating the generation of Lissajous curves using harmonic… Hilbert Curve Exploration SimulationNewThis simulation allows users to explore the properties of the Hilbert curve, a… Sin(x) Wave Exploration – Advanced MathematicsNewThis simulation visualizes the behavior of the sine function (sin(x)) across a wide range of… Mathematics Visualization SimulatorNewThis simulation provides interactive visualizations of various mathematical concepts,… Array Indexing SimulationNewThis simulation demonstrates the concept of indexing within a data structure. It's an… Bee Colony SimulationNewThis simulation demonstrates the concept of indexing and data organization. It's a… Ares Colony Robot IndexNewThis simulation demonstrates a basic exploration of an index value. It's designed to… Index 6 Spatial SimulationNewThis simulation explores the concept of indices in a 3D environment, potentially related to… Index Nine SimulationNewThis simulation presents a basic interactive visualization of numerical data represented as… Indexed Data VisualizationNewThis simulation presents a visual representation of data indexed from 101 to 150. It's… Zero-Based Index Data VisualizationNewThis simulation demonstrates a visual representation of data indexed from 0 to 49. It's… Three.js Indexing Data GalleryNewThis simulation presents a visual representation of data indexed from 0 to 49. It's designed… Index Data From Fifty To One HundredNewThis simulation demonstrates a visual representation of data indexed from 51 to 100. It's… Julia SetNewAn interactive 2D simulation visualizing and manipulating the Julia set, a classic example… Koch Curve ExplorationNewThis simulation explores the mathematical concept of the Koch curve by visually… Koch Snowflake FractalNewAn interactive 2D simulation demonstrating the construction of a Koch snowflake fractal… Linear Algebra VisualizerNewThis simulation visually represents fundamental concepts in linear algebra, including… Linear Programming Explained — Simplex, Duality, and GeometryNewThis simulation demonstrates the principles of linear programming through an interactive… Linear Regression SimulationNewThis simulation allows you to explore linear regression by observing how best-fit lines are… Linguistics Historical Linguistics SimulationNewThis simulation allows users to investigate the evolution of languages through historical… Linguistics Semantics SimulationNewThis simulation focuses on semantics – the study of meaning in language. Users can explore… Linguistics Syntax Analysis SimulationNewThis simulation introduces users to syntax analysis – the study of sentence structure. It… Lissajous Curves Harmonic OscillationsNewThis simulation allows you to visualize and manipulate Lissajous curves – elegant… Lissajous Curves & Parametric Equations — Interactive Oscillation SimulatorNewThis simulation allows users to explore Lissajous curves and parametric equations through an… Lissajous Curve GeneratorNewThis simulation allows you to generate Lissajous curves by manipulating the frequencies of… Enhanced Lissajous Curve GeneratorNewThis simulation allows you to precisely control the amplitude and frequency of two harmonic… Lissajous 3DNewThis simulation generates Lissajous curves in three dimensions, showcasing the mathematical… Lissajous CurvesNewThis simulation demonstrates Lissajous curves in a two-dimensional plane, illustrating… Management Decision Making SimulationNewThis simulation focuses on the process of making informed decisions within a business… Mandelbrot Set IterationNewExplore the mesmerizing Mandelbrot set through interactive iteration. This simulation allows… Mandelbrot ExplorerNewAn interactive 2D simulation visualizing the Mandelbrot set and its complex geometry. Mandelbrot InteractiveNewA 2D simulation allowing users to explore the Mandelbrot set in real-time with adjustable… Marching Squares MetaballsNewAn interactive 2D simulation combining marching squares with metaball modeling to create… Interactive Quadratic Equation SolverNewThis interactive simulation allows you to explore the solutions of a quadratic equation by… Mathematical Functions and Graph Analysis SimulationNewThis simulation allows users to dynamically explore the relationship between mathematical… Mathematical Modeling Research CenterNewThis simulation explores the application of mathematical modeling techniques to various… Mathematics Calculus SimulationNewThis simulation demonstrates calculus concepts such as derivatives and integrals through… Mathematics Differential Equations SimulationNewThis simulation demonstrates differential equations and their solutions through interactive… Mathematics Linear Algebra SimulationNewThis simulation demonstrates the fundamental concepts of linear algebra through interactive… Mathematics Number Theory SimulationNewThis simulation introduces users to the fascinating world of number theory. It allows them… Mathematics Optimization SimulationNewThis simulation demonstrates optimization techniques such as gradient descent. Users can… Mathematics Probability SimulationNewThis simulation explores probability concepts through interactive experiments. Users can… Mathematics Research PlatformNewThis simulation provides an interactive platform for exploring mathematical concepts. Users… Calculus Exploration – Functions and DerivativesNewThis simulation provides a hands-on exploration of fundamental calculus concepts –… Pythagorean Theorem SimulatorNewThis simulation provides an immersive experience exploring geometric modeling and algebraic… Interactive Mathematics Simulator ExplorationNewThis simulation offers a dynamic way to understand core mathematical principles by allowing… Mathematics Statistics SimulationNewThis simulation introduces users to statistical concepts such as data analysis, hypothesis… Mathematics Topology SimulationNewThis simulation provides an interactive introduction to topology, exploring concepts like… Dynamic Matrix Multiplication VisualizationNewThis simulation visualizes the process of dynamic matrix multiplication, allowing users to… Rendering Smooth Deformable MetaballsNewThis simulation demonstrates the rendering of metaballs, which are smooth, deformable… Music Theory SimulationNewThis simulation provides an interactive exploration of fundamental music theory concepts.… Tessellation MorphNewThis simulation explores the concept of tessellations and how they can morph or change based… Penrose TilingNewThis simulation visualizes Penrose tiling, a non-periodic tiling pattern created by two… Mandelbrot 3D ZoomNewThis simulation demonstrates the Mandelbrot set and its complex fractal geometry through a… Möbius Strip AntsNewObserve how ants navigate a Möbius strip – a non-orientable surface – showcasing concepts of… Clockwork Orrery – Planetary Motion SimulationNewInteract with this simulation to visualize the movement of planets around a central sun,… Lindenmayer System Plant GrowthNewExplore the growth of plants using Lindenmayer systems, observing how branching and… Origami Folding Simulation: Fold SpeedNewOrigami Folding Simulation - this variant focuses on fold speed. Honeycomb Structure ExplorationNewThis simulation visually demonstrates the intricate hexagonal structure of a beehive… Clockwork Orrery – Newtonian Orbital ModelNewWitness planetary orbits in this simulation, adjusting parameters to understand how… Origami Box — Self-Folding PaperNewThis simulation explores the mechanics behind self-folding origami structures, demonstrating… Tesseract — 4D Hypercube RotationNewThis simulation allows you to rotate a tesseract – a four-dimensional hypercube – providing… Turing Pattern Reaction-DiffusionNewThis simulation explores Turing patterns, which arise from reaction-diffusion systems. It… Honeycomb Growth: Cellular AutomataNewThis simulation visualizes the emergent growth patterns of honeycombs through a cellular… Infinite Spiral StaircaseNewThis simulation demonstrates the concept of infinite spirals, showcasing how mathematical… Turing Reaction-Diffusion SimulationNewThis simulation recreates Turing reaction-diffusion systems, illustrating how chemical… Origami Paper FoldNewThis interactive simulation guides users through the process of folding origami paper,… Orrery Mechanical ClockNewThis simulation recreates the workings of an orrery, a mechanical model of the solar system.… Newton Fractal Explorer – Complex Roots & Basin BoundariesNewThis simulation allows users to explore the dynamics of the Newton fractal. It demonstrates… Number Theory Explained — Primes, GCD, and Modular ArithmeticNewThis simulation offers an interactive exploration of fundamental number theory concepts.… Orebody Wireframe SlicingNewThis simulation allows users to visualize and interact with an orebody represented as a… Partial Differential Equations — Heat, Wave, and LaplaceNewThis simulation visualizes the solutions of fundamental partial differential equations,… PCA Dimensionality Reduction - Interactive VisualizationNewThis simulation demonstrates the application of Principal Component Analysis (PCA) for… Pca SimulationNewThis simulation allows users to explore Principal Component Analysis (PCA) by visualizing… PCA Visualization - Dimensionality ReductionNewThis simulation visually represents the process of PCA for dimensionality reduction. It… Phase Lumen | Three.jsNewThis simulation visually represents the concept of phase space in three dimensions using the… Phyllotaxis & Golden Angle Spiral — Interactive Sunflower SimulationNewThis simulation models the phyllotactic arrangement of leaves in a sunflower. It illustrates… Pythagorean Theorem Interactive SimulationNewThis interactive simulation visually demonstrates the Pythagorean theorem by allowing users… Reaction Diffusion Pattern LabNewThis simulation explores reaction-diffusion systems, a mathematical model used to explain… 3D Eclipse Geometry SimulatorNewVisualize the geometry of solar eclipses with this interactive simulation. Users can… Recursive Tree GeneratorNewThis simulation showcases recursive tree generation, a process where trees are built by… Regression SimulatorNewThis simulation illustrates the concept of regression analysis by allowing users to… Research Data Collection SimulationNewThis simulation demonstrates the process of collecting research data, highlighting various… Research Hypothesis Testing SimulationNewThis simulation guides users through the process of formulating a hypothesis, designing an… S35 Mandelbulb 3D ExplorerNewThis simulation generates a mesmerizing Mandelbrot set fractal in three dimensions. It… S50_06_Origami FoldingNewThis simulation demonstrates the principles of origami by allowing users to manipulate… Origami Folding PatternsNewExplore a variety of classic origami patterns in this simulation; adjust angles and folds to… Sacred GeometryNewThis simulation explores the concept of sacred geometry, showcasing how geometric patterns… Sierpinski Fractal GeneratorNewThis simulation creates the iconic Sierpinski triangle fractal through iterative removal of… Mandelbulb Fractal: Iterative CalculationNewMandelbulb Fractal - this variant focuses on iterative calculation. Sine Wave Curve PlotterNewThis simulation allows you to explore the relationship between the amplitude and frequency… Enhanced Sine Wave Curve PlotterNewThis simulation allows users to visually explore the behavior of sine waves by adjusting key… Spring LatticeNewThis simulation allows you to explore the behavior of a spring lattice – a network of… Bayesian vs Frequentist Statistics — Concepts and ComparisonsNewThis simulation provides an interactive comparison of Bayesian and frequentist statistical… Regression Analysis Explained — Linear Models and AssumptionsNewThis simulation demonstrates the principles of linear regression analysis, including the… Tesseract 4DNewThis simulation explores a visualization of a tesseract in four dimensions. It demonstrates… Tesseract ProjectionNewThis simulation visualizes the projection of a tesseract into three dimensions. It… Topology Explained — Continuity, Compactness, and ConnectednessNewThis simulation introduces the core ideas of topology – continuity, compactness, and… Tower Stability SimulatorNewThis simulation explores the principles of structural stability and equilibrium. Users can… t-SNE VisualizationNewThis simulation demonstrates the t-distributed stochastic neighbor embedding (t-SNE)… t-SNE Dimensionality ReductionNewThis simulation demonstrates the t-distributed stochastic neighbor embedding (t-SNE)… Ulam Spiral Mathematical PatternNewThis simulation allows you to create and explore Ulam Spirals, a visual representation of… Voronoi Diagrams & Delaunay TriangulationNewThis simulation allows users to generate Voronoi diagrams and Delaunay triangulations. It… Voronoi Shatter: Thermodynamic Fragmentation SimulationNewThis simulation explores the Voronoi diagram concept through a shattering effect. Users can… Wollastonite Acicular ClassificationNewThis simulation explores the structure of wollastonite minerals, focusing on their acicular… Category Theory ExplorerNewInteractive 3D category-theory diagram: place objects as spheres, click two objects to draw… Convex Optimization: Gradient Descent LandscapeNewA ball performs real gradient descent (x_new = x - alpha*grad f(x)) down a 3D convex bowl to… Galois Theory: Root Permutations & Solvability in Radicals SimulatorNewPlots the complex roots of a degree 3-5 polynomial on the complex plane and animates the… Homology Theory: Simplicial Complex BuilderNewBuild a simplicial complex in 3D by adding vertices, edges and filled triangles, and watch… Integer Programming: Branch & BoundNewAnimated 3D branch-and-bound search tree for integer linear programming: each node solves an… Manifolds & Parallel Transport SimulatorNewPick a point on a sphere, torus, saddle or plane and build its tangent plane from the… Propositional Logic Builder: Truth Tables, Parse Trees & Natural DeductionNewInteractive propositional-logic constructor: click variable (A/B/C) and operator buttons… Measure Theory: Riemann vs LebesgueNewInteractive canvas demo comparing Riemann integration (x-axis partitioning) against Lebesgue… Modular Forms — Fundamental Domain ExplorerNewInteractive fundamental-domain explorer for the modular group SL(2,Z) acting on the upper… Sheaf Gluing Axiom: Local Sections on an Overlapping CoverNewInteractive demonstration of the sheaf gluing axiom on the circle S1 covered by 4… Dimensional Dimension Fusion SimulationNewThis simulation investigates the process of merging or fusing different dimensions. Users… Newtons CradleNewThe simulation visually represents Newton's Cradle, demonstrating the conservation of… Pendulum WaveNewThis simulation demonstrates the principles of wave motion through a simple pendulum. Users… Standing Wave StringNewThis simulation demonstrates the principles of standing waves on a string. It illustrates… Terrain GenerationNewThis simulation demonstrates procedural terrain generation techniques, showcasing how…