📐 Matematyka i Analiza

Fractal ExplorerPopularne📱Mandelbrot and Julia sets rendered with smooth-colouring GLSL shaders. Pan, zoom, switch… Origami Box — Self-Folding Paper (2D)New📱A real crease-pattern simulation of a self-folding origami box in 2D: watch a flat square… Kaleidoscope Drawing: Mirror Symmetry Art (2D)New📱Draw freehand strokes on a 2D canvas and watch them replicate instantly into true N-fold… Pythagoras Tree (2D)New📱A 2D Canvas simulation that builds the Pythagoras tree fractal from real recursive squares:… Collatz Sequence Graph (2D)New📱Enter a starting number and watch its Collatz (3n+1) hailstone sequence unfold step by step… Taylor Series Plot (2D)New📱A 2D Canvas plot that builds the Taylor polynomial for sin(x), cos(x), exp(x), or ln(1+x)… Matrix Transformations (2D)New📱Drag four sliders to build any 2x2 matrix and watch it transform a shape, the coordinate… Riemann Sum — Rectangle Approximation (2D)New📱Choose a function and an integration rule, drag the interval sliders and the rectangle-count… Klein Bottle Fundamental Polygon (2D)New📱The 2D fundamental-polygon model of the Klein bottle: a square whose left and right edges… Fourier Coefficient Integrator (2D)New📱Numerically integrates the Fourier coefficients a_n and b_n of a square, sawtooth, or… 2D SVD: Singular Value Decomposition Step-by-Step (2D)New📱Watch a 2x2 matrix transform the unit circle into an ellipse through singular value… Sieve of Eratosthenes (2D)New📱Watch the classic Sieve of Eratosthenes run live on a 2D number grid: step through the… Fundamental Polygon Genus Explorer (2D)New📱Explore genus-g surfaces through their fundamental polygon: a 4g-sided polygon with edges… Newton's Fractal (2D)New📱A real per-pixel Newton's-method root-finding fractal rendered on a 2D canvas. Choose a… Brouwer Fixed Point Theorem (2D)New📱Click inside a 2D disk to drop a test point and watch it iterate under a continuous self-map… Eigenvalues & Eigenvectors 2D Visualizer (2D)New📱Interactively adjust a 2x2 matrix on a Canvas2D grid and watch its eigenvalues,… Riemann Integral Rectangles (2D)New📱Build Riemann sums by hand: pick a function, drag the interval bounds, and switch between… Fourier Transform (2D)New📱Build a time-domain signal from up to eight adjustable sine harmonics, or pick a classic… Power Iteration: Finding Eigenvectors (2D)New📱Watch a vector converge onto a matrix's dominant eigenvector through repeated power… SVD Image Compression (2D)New📱Watch a real singular value decomposition rebuild a grayscale test image rank by rank. Drag… Diffusion-Limited Aggregation (2D)New📱Watch random-walking particles drift in from the edge of the canvas and stick on contact… STFT Spectrogram Visualiser: Time-Frequency Analysis (2D)New📱Build a real Short-Time Fourier Transform spectrogram on Canvas2D: time runs left to right,… 2D Hilbert Curve Simulator (2D)New📱Watch a real Hilbert space-filling curve draw itself in 2D using the classic bit-based d2xy… Ulam Spiral — Patterns in the Primes (2D)New📱Watch integers spiral outward in a square grid while real prime numbers, found with a… Mandelbrot / Multibrot Set (2D)New📱The real 2D Mandelbrot set: z is iterated as z^n + c per pixel with a true escape-time… Wolfram 1D Cellular Automata (2D)New📱Explore all 256 Wolfram elementary cellular automaton rules on a Canvas2D grid. Watch Rule… Complex Functions (2D)New📱A 2D Canvas domain-coloring visualiser for complex functions. Hue encodes the argument and… 2D Harmonograph — Damped Pendulum Simulator (2D)New📱Trace real damped-oscillator superposition curves on a Canvas2D harmonograph. Adjust the… Phase Portrait — Vector Field & Trajectories (2D)New📱Draw the phase plane of a 2D dynamical system on Canvas2D: correctly computed vector-field… Sand Pile Model — Abelian Sandpile Cellular Automaton (2D)New📱A 2D Canvas simulation of the classic Bak-Tang-Wiesenfeld abelian sandpile: an integer grid… 2D Cellular Automaton: Birth/Survival DynamicsNew📱A 2D grid cellular automaton showing how selectable birth/survival rules like Conway's Game… Continued Fractions: Best Rational Approximations (2D)New📱Canvas2D lab that unfolds a real number into a continued fraction and shows its convergents… Standing Wave on a String (2D)New📱A 2D canvas simulation of a standing wave on a fixed-end string, with adjustable harmonic… Clockwork Orrery: Gear-Driven Planetary Motion (2D)New📱2D top-down orrery: six planets orbit at their true relative periods, driven by a visible… Fourier Epicycles (2D) — Drawing with Rotating CirclesNew📱A 2D canvas drawer that reconstructs a preset or hand-drawn closed shape as an animated… Knot Theory 2D — Crossing Diagrams & InvariantsNew📱Rotate a flattened knot diagram and watch crossings flip over/under while crossing number,… Linear Algebra Simulator (2D)New📱A Canvas2D 2x2 matrix-transform lab showing the deforming grid, basis vectors, eigenvectors… Newton Fractal 2D — Basins of AttractionNew📱Canvas2D lab where every pixel iterates Newton's method toward a complex root, colored by… Torus & Surface Genus (2D) — Topology of Orientable SurfacesNew📱Canvas2D lab that lets you switch between sphere, torus and double-torus meshes and view… Derivative Visualizer 2D: Numeric vs Analytic SlopeNew📱Canvas2D companion to the derivative visualizer: drag x0, shrink h and watch the secant… Gaussian Curvature & Geodesics (2D)New📱2D top-down curvature map: a (u,v) domain colored point-by-point by its analytically… Power Iteration: Watching a Vector Converge to a Dominant Eigenvector (2D)New📱2D power-iteration lab: a unit vector is repeatedly multiplied by a 2×2 matrix and… Möbius Strip Unrolled: Fundamental-Polygon & Twist Diagram (2D)New📱2D Möbius-strip companion: the strip unrolled into its flat fundamental polygon with an edge… Search Space Analysis: Hyperparameter Sampling Strategies (2D)New📱2D companion to the 3D hyperparameter search-space lab: the identical closed-form loss… Spirograph - Hypotrochoid Pattern Generator (2D)New📱Interactive 2D spirograph: drag the outer-radius, inner-radius, pen-offset and speed sliders… Tessellation Morph 2D: Polar-Equation Regular-Polygon TilingNew📱2D companion to Tessellation Morph: a lattice of cells traced from the exact polar equation… 3D Linear Algebra VisualizerNewDrag a real 3×3 matrix's nine entries in WebGL and watch a cubic lattice, the three basis… 3D Pythagorean Theorem SimulationNewA right-angle tetrahedron in real WebGL with three mutually perpendicular edges p, q, r from… 3D Sine Wave Surface Plotter — y = A·sin(Bx)·cos(Cz)New📱3D companion to the 2D sine wave plotter: the exact same y = A·sin(Bx) term, extended across… Chain Polymerization: Free-Radical Kinetics & Molecular Weight Distribution (2D)New📱2D chain-growth polymerization lab with a kinetic Monte-Carlo model of initiation,… Geometallurgical Block Model: IDW Ore-Grade Estimation (2D)New📱2D block-model estimator: sparse drill-hole assays are spread across a grade grid with real… Hypocycloids & Epicycloids — Rolling Circle Constraint (2D)New📱Watch a small circle roll without slipping inside or outside a fixed circle: its spin angle… Sacred Geometry: Flower of Life & Metatron's Cube Builder (2D)New📱2D sacred-geometry construction lab with a real hexagonal circle-packing (triangular… Sierpinski Tetrahedron Cross-Sections (2D)New📱2D companion to the 3D Sierpinski chaos game: slice a plane through the tetrahedral point… Armillary Sphere: Celestial Circles (2D Meridian Diagram)New📱A flat meridian-plane companion to the 3D armillary sphere: the same horizon, equator, polar… Fractal Tree Generator (2D)New📱A 2D canvas L-system fractal tree: adjust branch angle, length ratio and recursion depth to… Platonic Solids Duality (2D)New📱An interactive 2D Schlegel-diagram companion that flattens each Platonic solid into a planar… Bézier Curve Editor — Animated De Casteljau Construction (2D)NewA 2D companion to the 3D Bézier Curves simulator: drag control points on a plain canvas… 2D Spirograph — Rolling Circle Hypotrochoid & EpitrochoidNew📱A 2D companion to the 3D Spirograph simulator: watch the rolling circle itself trace the… 2D Fractal ExplorerNew📱A genuine per-pixel Mandelbrot and Julia set explorer on a plain 2D canvas: zoom recomputes… 2D Geodesic Dome Net — Flattened Icosahedron SubdivisionNew📱2D orthographic-projection companion to the 3D geodesic dome builder: real icosahedron… 2D Map Projections — Mercator vs Mollweide vs OrthographicNew📱A real 2D map-projection calculator: five forward-projection formulas (Equirectangular,… 2D Number Spirals — Ulam & Sacks Prime PlotNew📱A flat 2D canvas plot of the Ulam and Sacks number spirals with a real Sieve of Eratosthenes… 2D Voronoi DiagramNew📱A real per-pixel 2D Voronoi tessellation computed by brute-force nearest-site search, with… 2D Barnsley FernNew📱Watch the real Barnsley fern IFS grow point by point in 2D via the chaos-game algorithm.… Soroban Abacus Calculator (2D)NewInteractive 2D soroban abacus: drag beads on each rod toward the beam to build a number,… Group Multiplication Explorer (2D)New📱Interactive 2D Cayley-graph explorer: click elements of a cyclic or dihedral group to see… Set Operations Explorer: 2D Venn DiagramsNew📱Build two finite sets A and B as draggable, zoomable point clouds inside overlapping… Discriminant Analysis 2D: LDA vs QDA on Correlated Gaussian ClustersNew📱Two correlated bivariate-Gaussian classes with live covariance ellipses and the exact Bayes… Principle of Least Action: Path Relaxation (2D)New📱A 2D vertex-mesh companion to the 3D least-action gradient-descent solver: drag path nodes… Cross-Correlation Explorer (2D): Finding Lead-Lag Relationships Between Two Time SeriesNew📱Interactive 2D simulator: generate two related synthetic time series with a hidden lag… Fundamental Group of the Punctured PlaneNew📱Draw a closed loop on a 2D canvas around 2-4 punctures in a plane and watch its homotopy… New Year Spiral: The Golden Ratio in TimeNew📱A real logarithmic spiral r = a·e^(bθ) plotted in 2D with pan/zoom, next to a live… New Year Spiral: The Golden Ratio in TimeNew📱A real logarithmic spiral r = a·e^(bθ) rendered as a rising 3D helix (one turn per year)… Gift Wrapping: Minimal Surface & Packing MathNew📱A 2D blueprint of the real minimum-wrapping-paper formula for a box, plus a genuine 2D shelf… Gift Wrapping: Minimal Surface & Packing MathNew📱Derive the real minimum-wrapping-paper formula for a box and watch a genuine extreme-point… KdV Two-Soliton Collision — Finite-Difference Solver (2D)New📱Watch the Korteweg-de Vries equation solved directly by finite differences (the 1965… Dyson Brownian Motion: Eigenvalues in MotionNew📱2D companion to the Wigner semicircle law simulator: integrate Dyson's 1962 Brownian-motion… Brachistochrone Spectral Ritz Flow (2D)New📱A 2D spectral counterpart to the brachistochrone gradient flow: the trial curve is built… Mean Value Theorem Explorer (2D)New📱Drag the endpoints of an interval directly on a 2D function graph and watch a second panel… Isoperimetric Flow: Why the Circle WinsNew📱Watch a closed curve evolve under a length-preserving gradient flow derived from the… ODE Integrator Race — Euler vs RK2 vs RK4New📱Three ODE integrators — Euler, midpoint (RK2) and classical Runge-Kutta (RK4) — solve the… Gram-Schmidt Orthogonalization in 2DNew📱Drag vector tips on a 2D plane and watch the real Gram-Schmidt process build an orthonormal… Mann-Whitney U Test: Beeswarm & Permutation Null (2D)New📱Interactive 2D Mann-Whitney U test: two samples are laid out on a real-valued beeswarm axis… Chinese Remainder Theorem — Modular Rings (2D)New📱Three concentric rotating rings with coprime prime sector counts spin under a shared… Poincaré Index Theorem: Vector Fields on a Disk (2D)New📱Interactive 2D companion to the Hairy Ball theorem: a real gradient vector field lives on a… Quasi-Monte Carlo 2D: Point-Set Discrepancy RaceNew📱Race a pseudorandom Monte Carlo sampler against a 2D Halton low-discrepancy sequence side by… CLT Convergence-Rate Diagnostic (2D log-log)New📱A 2D companion to the 3D CLT histogram: eight sample sizes (n=4..512) are simulated… Torus Knots as Braid Closures: Crossing Number & WritheNew📱Builds the standard braid word (sigma_1...sigma_(p-1))^q for a torus knot T(p,q), closes it… 2D Frenet Frame: Signed Curvature & the Evolute of a Plane CurveNew📱Watch the moving tangent-normal frame travel along an ellipse, limaçon or 3-petal rose, with… Pointwise vs Uniform Convergence — 2D Trace ViewNew📱A 2D companion view of pointwise vs uniform convergence: watch the curve f_n(x) settle… Spectral Projection & Eigenfunction DynamicsNew📱Project a target function onto an orthonormal basis of sin(nx) in Hilbert space. Adjust the… Spectral Projection & Eigenfunction DynamicsNew📱Visualize time-evolution of eigenfunctions sin(nx) as oscillating ribbons along a… Gram-Schmidt Orthogonalization in 3DNew📱Drag two 3D vectors and watch the Gram-Schmidt process build an orthonormal basis from them… Isoperimetric Flow: Why the Circle WinsNew📱Watch a closed curve evolve under a length-preserving gradient flow derived from the… Mann-Whitney U Test: Rank-Based Group ComparisonNew📱Interactive 3D Mann-Whitney U test: two samples are ranked jointly on a live rank track, and… Chinese Remainder Theorem — Modular Gear WheelsNew📱Three interlocking gear wheels with coprime prime tooth counts spin under a shared counter,… Hairy Ball Theorem — Vector Fields on a SphereNew📱Comb a tangent vector field over a 3D sphere and watch the Hairy Ball / Poincaré–Hopf… Pointwise vs Uniform ConvergenceNew📱Explore a 3D waterfall of a function sequence f_n(x) and test, with a live epsilon-band and… Quasi-Monte Carlo: Low-Discrepancy vs Pseudorandom IntegrationNew📱Race a pseudorandom Monte Carlo sampler against a Halton low-discrepancy sequence as both… Central Limit Theorem Breakdown: Heavy-Tailed ConvergenceNew📱Draw sample means from Gaussian, Exponential and Pareto sources with tunable tail heaviness… Torus Knots: Writhe & Crossing-Sign ExplorerNew📱Renders a real torus knot T(p,q) and computes its crossing count and writhe live from the… Brachistochrone Gradient FlowNew📱Watch a roughly guessed path relax, step by step, into the true brachistochrone curve as… Frenet–Serret Frame: Curvature & Torsion of a Space CurveNew📱Watch the moving tangent-normal-binormal frame travel along a helix, trefoil knot or torus… KdV Two-Soliton CollisionNew📱Exact Hirota two-soliton solution of the Korteweg-de Vries equation, rendered as a live 3D… Principle of Least Action: Path RelaxationNew📱Watch a randomly jagged 3D trial trajectory relax step by step into the true classical path… Discriminant Analysis: Classifying Correlated Gaussian ClustersNew📱Two correlated multivariate-Gaussian classes with live covariance ellipsoids and the exact… ODE Integrator Race — Euler vs RK2 vs RK4New📱Three ODE integrators — Euler, midpoint (RK2) and classical Runge-Kutta (RK4) — solve the… Random Matrix Theory: The Wigner Semicircle LawNew📱Build large random symmetric matrices, diagonalize them in the browser with a from-scratch… Mean Value Theorem ExplorerNew📱Drag the endpoints of an interval on a differentiable curve and watch a bisection search… Set Operations Explorer: 3D Venn DiagramsNew📱Build two finite sets A and B as glowing 3D point clouds, choose union, intersection,… Cross-Correlation Explorer: Finding Lead-Lag Relationships Between Two Time SeriesNew📱Generate two related synthetic time series with a hidden lag between them, then watch the… Fundamental Group of the Punctured PlaneNew📱Build a closed loop that winds around 2-4 punctures in a plane and watch its homotopy class… Cohomology ExplorerNew📱Build a genus-g handlebody as a simplicial mesh, paint a 1-cochain on its edges, apply the… Central Limit Theorem SimulatorNew📱Interactive Central Limit Theorem simulator: draw repeated samples from a uniform,… Collatz Conjecture Trajectory ExplorerNew📱Race dozens of Collatz (3n+1) hailstone sequences side by side in 3D and watch how chain… Phase Portraits & Numerical IntegrationNew📱Interactive 3D phase-plane simulation of differential equations: a direction-field grid, a… Gaussian Curvature & GeodesicsNew📱Watch a deformable parametric surface colored by its analytically computed Gaussian… Elliptic Curve ExplorerNew📱Interactive 3D exploration of the elliptic curve y² = x³ + ax + b: reshape the curve live… Graph Explorer: Shortest Path & ColoringNew📱Interactive 3D graph simulation that runs Dijkstra's shortest-path algorithm and a greedy… Calculator Pipeline SimulatorNew📱Interactive calculator pipeline: watch operand blocks flow down a conveyor into an operator… Calculus in 3D: Tangent Planes & Solids of RevolutionNew📱Interactive 3D calculus lab: watch a tangent plane track the gradient across a surface… Galois Theory: Root Permutations & Solvability in Radicals SimulatorNew📱Plots the complex roots of a degree 3-5 polynomial on the complex plane and animates the… Homology Theory: Simplicial Complex BuilderNew📱Build a simplicial complex in 3D by adding vertices, edges and filled triangles, and watch… Integer Programming: Branch & BoundNew📱Animated 3D branch-and-bound search tree for integer linear programming: each node solves an… Manifolds & Parallel Transport SimulatorNew📱Pick a point on a sphere, torus, saddle or plane and build its tangent plane from the… Propositional Logic Builder: Truth Tables, Parse Trees & Natural DeductionNew📱Interactive propositional-logic constructor: click variable (A/B/C) and operator buttons… Measure Theory: Riemann vs LebesgueNew📱Interactive canvas demo comparing Riemann integration (x-axis partitioning) against Lebesgue… Modular Forms — Fundamental Domain ExplorerNew📱Interactive fundamental-domain explorer for the modular group SL(2,Z) acting on the upper… Sheaf Gluing Axiom: Local Sections on an Overlapping CoverNew📱Interactive demonstration of the sheaf gluing axiom on the circle S1 covered by 4… Category Theory ExplorerNew📱Interactive 3D category-theory diagram: place objects as spheres, click two objects to draw… Convex Optimization: Gradient Descent LandscapeNew📱A ball performs real gradient descent (x_new = x - alpha*grad f(x)) down a 3D convex bowl to… Loss Landscape OptimizerNew📱Explore advanced mathematical topics in hyperparameter optimization. Learn about… Linear Algebra SimulatorNew📱Watch a 2x2 matrix transform a live vector grid in real time: see basis vectors,… Multi-Objective Optimization MathematicsNew📱Explore multi-objective optimization mathematics. Learn about Pareto optimality, Pareto… Search Space Analysis: Mathematics of Hyperparameter SpacesNew📱Learn about search space analysis in hyperparameter optimization. Understand dimensionality,… The Life-Cycle Math of ClothingNew📱An interactive 3D pipeline that turns fiber choice, dyeing intensity, shipping mode and… Algebraic Number Theory: Rings, Ideals and Number FieldsNew📱Explore the fundamental concepts of algebraic number theory through an interactive… Cyclic Group Zn — Cayley GraphNew📱Visualize 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 TheoremNew📱Interactive algebraic geometry: the Weierstrass cubic y² = x³+ax+b, a secant/tangent line… Algebraic Topology: Genus, Handles & Homology ExplorerNew📱Build a genus-g handlebody by attaching handles to a sphere and watch its homology… Analytic Number Theory: Prime Spiral & the Prime-Counting FunctionNew📱Watch a rising Sacks-style spiral of the integers light up with prime numbers. Sweep the… Complex Function VisualizerNew📱This simulation demonstrates how to visualize complex mathematical functions by coloring… ML Model Training: Apartment Price PredictionNew📱Explore how different training parameters – learning rates, epochs, and feature selection –… Spirograph - Hypotrochoid Pattern GeneratorNew📱This simulation illustrates the creation of intricate patterns using a spirograph,… Sunflower Field - Phyllotaxis PatternNew📱This simulation explores phyllotaxis, the arrangement of leaves around a stem in plants like… Impossible TriangleNew📱This simulation demonstrates the principles of Euclidean geometry and how it's impossible to… Thermal Fracture of a Voronoi RegionNew📱Explore the dynamic breakdown of a Voronoi diagram as it undergoes thermal stress,… Möbius Ant WalkNew📱This simulation explores the unique properties of a Möbius strip by visualizing an ant… Origami Crane Fold: Origami FoldingNew📱Explore the precise geometric transformations required to fold a traditional origami crane,… Abacus CalculationNew📱This simulation demonstrates the operation of an abacus as a tool for performing arithmetic… Spirograph Gear DrawingNew📱This simulation visually demonstrates the mathematical relationships behind spirograph… Recursive Fractal Tree SimulationNew📱Witness a visually captivating fractal tree evolve through mathematical recursion. Adjust… Fractal Branching DynamicsNew📱Observe the generation of complex fractal patterns via recursive branching, showcasing how… Mandelbrot ShaderNew📱This simulation generates a Mandelbrot set using a shader. It demonstrates the iterative… Kaleidoscope Geometric PatternsNew📱This simulation visualizes the patterns generated by a kaleidoscope. It demonstrates how… Three-Dimensional Kaleidoscope PatternsNew📱Explore the captivating visual effects generated by a rotating, geometric kaleidoscope… 3D Armillary SphereNew📱This simulation demonstrates the armillary sphere, a historical instrument used for… 3D Fractal ExplorerNew📱This interactive simulation explores the generation and visualization of fractals within a… 3D Fractal TreeNew📱This simulation visually represents the generation of fractal patterns using recursive… 3D Galton BoardNew📱This simulation allows you to explore the distribution of random outcomes produced by a… 3D Galton Board OskNew📱This simulation demonstrates the probabilistic nature of random walks and the distribution… 3D HarmonographNew📱A visual representation of complex mathematical functions through the movement of… 3D Knot TheoryNew📱This simulation explores the visual representation of knots in a three-dimensional space. It… 3D Lsystem Plant GrowthNew📱This simulation demonstrates the growth of plants using L-systems. Users can manipulate… 3D MandelbulbNew📱Witness the mesmerizing beauty of a Mandelbulb, a fractal shape generated by complex… 3D Menger SpongeNew📱This simulation demonstrates the growth of a Menger sponge in three dimensions. It allows… 3D Pascals TriangleNew📱This simulation visually represents Pascal’s triangle, showcasing the relationships between… 3D Platonic Solids DualityNew📱This simulation demonstrates the geometric relationships between platonic solids and their… 3D Prime Number SpiralNew📱This simulation generates a spiral pattern using prime numbers, visually representing the… Complex Origami Folding PatternsNew📱This simulation lets you explore intricate origami designs by manipulating virtual paper and… Mandelbulb Fractal: Mandelbrot SetNew📱Explore the mesmerizing Mandelbulb fractal, adjusting iteration limits and zoom levels to… Mandelbulb Fractal: ZoomNew📱Explore the mesmerizing Mandelbulb fractal in stunning detail with adjustable zoom levels,… Harmonograph: Rotating Cam SimulationNew📱Witness the creation of complex geometric patterns through a rotating cam mechanism,… Mandelbulb Fractal: Complex GeometryNew📱Explore the mesmerizing Mandelbulb fractal, adjusting its size and rotation speed to… Lissajous Sand Pendulum / HarmonographNew📱This simulation recreates the mesmerizing patterns produced by a Lissajous sand pendulum. It… Procedural SnowflakesNew📱This simulation demonstrates the generation of complex snowflake patterns using procedural… 3D Cellular Automaton: 3d DynamicsNew📱Explore emergent patterns in a 3D cellular automaton where cells interact based on simple… 3D Voronoi GrowthNew📱This simulation illustrates the concept of Voronoi diagrams and their growth patterns. Users… Sunflower PhyllotaxisNew📱This simulation explores the mathematical patterns governing the arrangement of sunflower… Nanotechnology in Crystal StructuresNew📱This simulation explores how manipulating nanomaterials within a crystalline structure… Advanced Mathematics - Comprehensive GuideNew📱This simulation demonstrates fundamental mathematical concepts through interactive… Boolean Algebra Explained — Logic, Gates, and SimplificationNew📱This simulation visually teaches the principles of Boolean algebra through interactive logic… Calculus Visualizer Derivatives IntegralsNew📱This interactive visualization allows you to explore the core concepts of calculus –… Cellular Automata Explained — Local Rules, Global PatternsNew📱This simulation illustrates the fascinating behavior of cellular automata. Users can… Chemistry-Computational-Chemistry-LabNew📱This simulator combines computational tools with a laboratory environment for exploring… Chromite Spiral SeparatorNew📱This simulation visualizes the complex geometry and flow patterns within a chromite spiral… Clifford AttractorNew📱This simulation explores the Clifford attractor, a complex mathematical system that… Collatz Conjecture: Iterative Number SequencesNew📱Visually trace the progression of a number through the Collatz conjecture, observing how it… Combinatorics Explained — Counting, Permutations, and GraphsNew📱This simulation demonstrates the fundamental concepts of combinatorics, including counting… Computational Mathematics - Comprehensive GuideNew📱This simulation demonstrates computational mathematics by showcasing numerical methods for… Correlation MatrixNew📱This simulation visualizes a correlation matrix, illustrating how different variables relate… Correlation Matrix Heatmap - Interactive Data AnalysisNew📱This simulation provides an interactive visualization of a correlation matrix, allowing… Data Distribution Explorer - Statistical VisualizationNew📱This simulation displays a visualization of a data distribution, offering insights into the… Data Distribution Explorer - Statistical Visualization ToolNew📱This simulation allows users to visualize the distribution of a dataset using various… Data Structures Explained — Arrays, Trees, Graphs, and HeapsNew📱This simulation provides an interactive visual explanation of fundamental data structures.… Delaunay MeshNew📱This simulation demonstrates the Delaunay triangulation algorithm, which creates a mesh of… Differential Equations Phase Portraits AnalysisNew📱This simulation allows you to explore complex systems by visualizing their solutions as… Differential Geometry Explained — Curves, Surfaces, and CurvatureNew📱This interactive simulation provides a visual introduction to differential geometry… Fourier Epicycles: A Visual ExplorationNew📱This simulation visually demonstrates the concept of epicycles, showcasing how ancient… Mandelbrot Set ExplorationNew📱Explore the mesmerizing world of fractal geometry! This simulation demonstrates how… Fractal Geometry Exploration SimulationNew📱Explore the fascinating world of fractal geometry by manipulating iteration depth and… Fractal Tree GenerationNew📱Explore the creation of intricate, self-similar tree structures using recursive algorithms… Fractals Explained: Self-Similarity and the Mandelbrot SetNew📱Explore the mesmerizing world of fractals with this simulation! Witness how the Mandelbrot… Galton Board SimulationNew📱Observe balls cascading through a peg board, demonstrating the binomial distribution and its… Gem Faceting SimulationNew📱This simulation allows users to explore the process of gem faceting, demonstrating how light… Gradient Descent Simulator - Optimization VisualizerNew📱This simulator visualizes the process of gradient descent optimization, allowing users to… Gradient Descent VisualizationNew📱This simulation visually represents the gradient descent optimization algorithm,… Harmonograph Lissajous CurvesNew📱An interactive 2D simulation demonstrating the generation of Lissajous curves using harmonic… Hilbert Curve Exploration SimulationNew📱This simulation allows users to explore the properties of the Hilbert curve, a… Sin(x) Wave Exploration – Advanced MathematicsNew📱This simulation visualizes the behavior of the sine function (sin(x)) across a wide range of… Mathematics Visualization SimulatorNew📱This simulation provides interactive visualizations of various mathematical concepts,… Array Indexing SimulationNew📱This simulation demonstrates the concept of indexing within a data structure. It's an… Bee Colony SimulationNew📱This simulation demonstrates the concept of indexing and data organization. It's a… Ares Colony Robot IndexNew📱This simulation demonstrates a basic exploration of an index value. It's designed to… Index 6 Spatial SimulationNew📱This simulation explores the concept of indices in a 3D environment, potentially related to… Index Nine SimulationNew📱This simulation presents a basic interactive visualization of numerical data represented as… Indexed Data VisualizationNew📱This simulation presents a visual representation of data indexed from 101 to 150. It's… Zero-Based Index Data VisualizationNew📱This simulation demonstrates a visual representation of data indexed from 0 to 49. It's… Three.js Indexing Data GalleryNew📱This simulation presents a visual representation of data indexed from 0 to 49. It's designed… Index Data From Fifty To One HundredNew📱This simulation demonstrates a visual representation of data indexed from 51 to 100. It's… Julia SetNew📱An interactive 2D simulation visualizing and manipulating the Julia set, a classic example… Koch Curve ExplorationNew📱This simulation explores the mathematical concept of the Koch curve by visually… Koch Snowflake FractalNew📱An interactive 2D simulation demonstrating the construction of a Koch snowflake fractal… Linear Algebra VisualizerNew📱This simulation visually represents fundamental concepts in linear algebra, including… Linear Programming Explained — Simplex, Duality, and GeometryNew📱This simulation demonstrates the principles of linear programming through an interactive… Linear Regression SimulationNew📱This simulation allows you to explore linear regression by observing how best-fit lines are… Linguistics Historical Linguistics SimulationNew📱This simulation allows users to investigate the evolution of languages through historical… Linguistics Semantics SimulationNew📱This simulation focuses on semantics – the study of meaning in language. Users can explore… Linguistics Syntax Analysis SimulationNew📱This simulation introduces users to syntax analysis – the study of sentence structure. It… Lissajous Curves Harmonic OscillationsNew📱This simulation allows you to visualize and manipulate Lissajous curves – elegant… Lissajous Curves & Parametric Equations — Interactive Oscillation SimulatorNew📱This simulation allows users to explore Lissajous curves and parametric equations through an… Lissajous Curve GeneratorNew📱This simulation allows you to generate Lissajous curves by manipulating the frequencies of… Enhanced Lissajous Curve GeneratorNew📱This simulation allows you to precisely control the amplitude and frequency of two harmonic… Lissajous 3DNew📱This simulation generates Lissajous curves in three dimensions, showcasing the mathematical… Lissajous CurvesNew📱This simulation demonstrates Lissajous curves in a two-dimensional plane, illustrating… Management Decision Making SimulationNew📱This simulation focuses on the process of making informed decisions within a business… Mandelbrot Set IterationNew📱Explore the mesmerizing Mandelbrot set through interactive iteration. This simulation allows… Mandelbrot ExplorerNew📱An interactive 2D simulation visualizing the Mandelbrot set and its complex geometry. Mandelbrot InteractiveNew📱A 2D simulation allowing users to explore the Mandelbrot set in real-time with adjustable… Marching Squares MetaballsNew📱An interactive 2D simulation combining marching squares with metaball modeling to create… Interactive Quadratic Equation SolverNew📱This interactive simulation allows you to explore the solutions of a quadratic equation by… Mathematical Functions and Graph Analysis SimulationNew📱This simulation allows users to dynamically explore the relationship between mathematical… Mathematical Modeling Research CenterNew📱This simulation explores the application of mathematical modeling techniques to various… Mathematics Calculus SimulationNew📱This simulation demonstrates calculus concepts such as derivatives and integrals through… Mathematics Differential Equations SimulationNew📱This simulation demonstrates differential equations and their solutions through interactive… Mathematics Linear Algebra SimulationNew📱This simulation demonstrates the fundamental concepts of linear algebra through interactive… Mathematics Number Theory SimulationNew📱This simulation introduces users to the fascinating world of number theory. It allows them… Mathematics Optimization SimulationNew📱This simulation demonstrates optimization techniques such as gradient descent. Users can… Mathematics Probability SimulationNew📱This simulation explores probability concepts through interactive experiments. Users can… Mathematics Research PlatformNew📱This simulation provides an interactive platform for exploring mathematical concepts. Users… Calculus Exploration – Functions and DerivativesNew📱This simulation provides a hands-on exploration of fundamental calculus concepts –… Pythagorean Theorem SimulatorNew📱This simulation provides an immersive experience exploring geometric modeling and algebraic… Mathematics Simulator with Live Geometry Area CalculatorNew📱This simulation offers a dynamic way to understand core mathematical principles by allowing… Mathematics Statistics SimulationNew📱This simulation introduces users to statistical concepts such as data analysis, hypothesis… Mathematics Topology SimulationNew📱This simulation provides an interactive introduction to topology, exploring concepts like… Dynamic Matrix Multiplication VisualizationNew📱This simulation visualizes the process of dynamic matrix multiplication, allowing users to… Rendering Smooth Deformable MetaballsNew📱This simulation demonstrates the rendering of metaballs, which are smooth, deformable… Music Theory SimulationNew📱This simulation provides an interactive exploration of fundamental music theory concepts.… Tessellation MorphNew📱This simulation explores the concept of tessellations and how they can morph or change based… Penrose TilingNew📱This simulation visualizes Penrose tiling, a non-periodic tiling pattern created by two… Mandelbrot 3D ZoomNew📱This simulation demonstrates the Mandelbrot set and its complex fractal geometry through a… Möbius Strip AntsNew📱Observe how ants navigate a Möbius strip – a non-orientable surface – showcasing concepts of… Clockwork Orrery – Planetary Motion SimulationNew📱Interact with this simulation to visualize the movement of planets around a central sun,… Lindenmayer System Plant GrowthNew📱Explore the growth of plants using Lindenmayer systems, observing how branching and… Origami Folding Simulation: Fold SpeedNew📱Adjust the folding speed and observe how it affects the geometry of complex origami models,… Honeycomb Structure ExplorationNew📱This simulation visually demonstrates the intricate hexagonal structure of a beehive… Clockwork Orrery – Newtonian Orbital ModelNew📱Witness planetary orbits in this simulation, adjusting parameters to understand how… Origami Box — Self-Folding PaperNew📱This simulation explores the mechanics behind self-folding origami structures, demonstrating… Tesseract — 4D Hypercube RotationNew📱This simulation allows you to rotate a tesseract – a four-dimensional hypercube – providing… Turing Pattern Reaction-DiffusionNew📱This simulation explores Turing patterns, which arise from reaction-diffusion systems. It… Honeycomb Growth: Cellular AutomataNew📱This simulation visualizes the emergent growth patterns of honeycombs through a cellular… Infinite Spiral StaircaseNew📱This simulation demonstrates the concept of infinite spirals, showcasing how mathematical… Turing Reaction-Diffusion SimulationNew📱This simulation recreates Turing reaction-diffusion systems, illustrating how chemical… Origami Paper FoldNew📱This interactive simulation guides users through the process of folding origami paper,… Orrery Mechanical ClockNew📱This simulation recreates the workings of an orrery, a mechanical model of the solar system.… Newton Fractal Explorer – Complex Roots & Basin BoundariesNew📱This simulation allows users to explore the dynamics of the Newton fractal. It demonstrates… Number Theory Explained — Primes, GCD, and Modular ArithmeticNew📱This simulation offers an interactive exploration of fundamental number theory concepts.… Partial Differential Equations — Heat, Wave, and LaplaceNew📱This simulation visualizes the solutions of fundamental partial differential equations,… PCA Dimensionality Reduction - Interactive VisualizationNew📱This simulation demonstrates the application of Principal Component Analysis (PCA) for… Pca SimulationNew📱This simulation allows users to explore Principal Component Analysis (PCA) by visualizing… PCA Visualization - Dimensionality ReductionNew📱This simulation visually represents the process of PCA for dimensionality reduction. It… Phyllotaxis & Golden Angle Spiral — Interactive Sunflower SimulationNew📱This simulation models the phyllotactic arrangement of leaves in a sunflower. It illustrates… Pythagorean Theorem Interactive SimulationNew📱This interactive simulation visually demonstrates the Pythagorean theorem by allowing users… Recursive Tree GeneratorNew📱This simulation showcases recursive tree generation, a process where trees are built by… Regression SimulatorNew📱This simulation illustrates the concept of regression analysis by allowing users to… Research Data Collection SimulationNew📱This simulation demonstrates the process of collecting research data, highlighting various… Research Hypothesis Testing SimulationNew📱This simulation guides users through the process of formulating a hypothesis, designing an… S35 Mandelbulb 3D ExplorerNew📱This simulation generates a mesmerizing Mandelbrot set fractal in three dimensions. It… S50_06_Origami FoldingNew📱This simulation demonstrates the principles of origami by allowing users to manipulate… Origami Folding PatternsNew📱Explore a variety of classic origami patterns in this simulation; adjust angles and folds to… Sacred GeometryNew📱This simulation explores the concept of sacred geometry, showcasing how geometric patterns… Sierpinski Fractal GeneratorNew📱This simulation creates the iconic Sierpinski triangle fractal through iterative removal of… Mandelbulb Fractal: Iterative CalculationNew📱Explore the mesmerizing Mandelbulb fractal by adjusting iteration counts and observing its… Sine Wave Curve PlotterNew📱This simulation allows you to explore the relationship between the amplitude and frequency… Enhanced Sine Wave Curve PlotterNew📱This simulation allows users to visually explore the behavior of sine waves by adjusting key… Bayesian vs Frequentist Statistics — Concepts and ComparisonsNew📱This simulation provides an interactive comparison of Bayesian and frequentist statistical… Regression Analysis Explained — Linear Models and AssumptionsNew📱This simulation demonstrates the principles of linear regression analysis, including the… Tesseract 4DNew📱This simulation explores a visualization of a tesseract in four dimensions. It demonstrates… Tesseract ProjectionNew📱This simulation visualizes the projection of a tesseract into three dimensions. It… Topology Explained — Continuity, Compactness, and ConnectednessNew📱This simulation introduces the core ideas of topology – continuity, compactness, and… t-SNE VisualizationNew📱This simulation demonstrates the t-distributed stochastic neighbor embedding (t-SNE)… t-SNE Dimensionality ReductionNew📱Explore t-SNE's non-linear dimensionality reduction, visualizing high-dimensional MNIST… Ulam Spiral Mathematical PatternNew📱This simulation allows you to create and explore Ulam Spirals, a visual representation of… Voronoi Diagrams & Delaunay TriangulationNew📱This simulation allows users to generate Voronoi diagrams and Delaunay triangulations. It… Voronoi Shatter: Thermodynamic Fragmentation SimulationNew📱This simulation explores the Voronoi diagram concept through a shattering effect. Users can… Wollastonite Acicular ClassificationNew📱This simulation explores the structure of wollastonite minerals, focusing on their acicular… Dimensional Dimension Fusion SimulationNew📱This simulation investigates the process of merging or fusing different dimensions. Users… Interactive Pendulum Momentum TransferNew📱The simulation visually represents Newton's Cradle, demonstrating the conservation of… Pendulum WaveNew📱This simulation demonstrates the principles of wave motion through a simple pendulum. Users… Standing Wave StringNew📱This simulation demonstrates the principles of standing waves on a string. It illustrates… Terrain GenerationNew📱This simulation demonstrates procedural terrain generation techniques, showcasing how… Chain PolymerizationNew📱This simulation demonstrates the process of chain polymerization, where small monomers… Geological Block ModelNew📱This simulation allows users to visualize and interact with a geological block model – a… Geometallurgical Block ModelNew📱This simulation demonstrates the creation and application of a geometallurgical block model.… Orebody Wireframe SlicingNew📱This simulation allows users to visualize and interact with an orebody represented as a… Phase Lumen | Three.jsNew📱This simulation visually represents the concept of phase space in three dimensions using the… Reaction Diffusion Pattern LabNew📱This simulation explores reaction-diffusion systems, a mathematical model used to explain… 3D Eclipse Geometry SimulatorNew📱Visualize the geometry of solar eclipses with this interactive simulation. Users can… Spring LatticeNew📱This simulation allows you to explore the behavior of a spring lattice – a network of… Tower Stability SimulatorNew📱This simulation explores the principles of structural stability and equilibrium. Users can… The Derivative as a LimitNew📱Interactive 3D curve where dragging a secant line's second point closer to a fixed point… Eigenvalues and Eigenvectors: The Directions a Matrix Refuses to RotateNew📱Interactive 3D vector field where adjusting a transformation matrix's entries shows most… Prime Distribution and GapsNew📱Interactive 3D number-line visualization where scrubbing through increasing ranges of… Wallpaper Symmetry Group ExplorerNew📱Interactive 3D tiled plane where switching among the 17 wallpaper groups shows how rotation,… Voronoi & Lloyd's Relaxation ExplorerNew📱Interactive 3D point set where running Lloyd's relaxation iterations shows how Voronoi cells… Riemann Zeta Critical Strip ExplorerNew📱Interactive 3D complex plane where sweeping through the critical strip shows how the Riemann… Buffon's NeedleNew📱Drop random needles onto a floor ruled with parallel lines and watch pi emerge from the… Dragon CurveNew📱Generate the Heighway dragon curve from its recursive L/R turn-sequence doubling rule and… Fibonacci Spiral — Golden Ratio VisualizerNew📱Explore the Fibonacci spiral, the golden angle, and the golden ratio φ≈1.618034 with an… Ford Circles & Farey SequenceNew📱Every reduced fraction p/q between 0 and 1 has a Ford circle tangent to the number line at… Koch SnowflakeNew📱Build the Koch snowflake by recursively replacing the middle third of every segment with an… Monte Carlo Pi EstimationNew📱Estimate the value of pi by scattering random points into a square and counting how many… Pascal's Triangle mod pNew📱Compute binomial coefficients C(n,k) modulo a small prime and colour each cell by its… Peano Space-Filling CurveNew📱Watch Giuseppe Peano's 1890 space-filling curve unfold through a recursive 3x3 boustrophedon… Platonic SolidsNew📱Interactive Platonic solids explorer. Rotate wireframe or solid-shaded tetrahedra, cubes,… Recamán's Sequence VisualizationNew📱Observe Recamán's Sequence develop dynamically, with arcs representing each term, and adjust… Sierpinski CarpetNew📱Recursively subdivide a square into a 3x3 grid, removing the center square at every level,… Wallpaper Symmetry GroupsNew📱Nine of the 17 mathematically possible wallpaper groups, built by tiling an asymmetric motif… Derivative VisualizerNew📱Slide the point x0 and shrink the step h to watch a secant line collapse onto the tangent,… Brouwer Fixed Point TheoremNew📱Stir and squash a disc onto itself and see why at least one point always stays put, the… Bézier CurvesNew📱Drag control points and step the de Casteljau construction to see how a Bezier curve is… Soap Bubble — Minimal Surface ExplorationNew📱Simulate soap films finding minimal surfaces. Plateau relaxation minimizes surface area.… 3D Cellular Automaton — Survival/Birth RulesNew📱Explore 3D cellular automata with Moore neighborhood (26 neighbors). Famous rules: Cloud,… Hyperbolic Geometry TilingNew📱Tessellate the Poincaré disk model of hyperbolic plane with {p,q} regular tilings. Möbius… p-adic Number Ultrametric SpaceNew📱Visualize p-adic numbers as a fractal tree. The p-adic distance |x-y|_p = p^{-v_p(x-y)}… Prime Distribution & GapsNew📱Visualize prime number distribution: spiral (Ulam), prime gaps histogram, and the Prime… Weierstrass Nowhere-Differentiable FunctionNew📱The Weierstrass function W(x) = Σ aⁿ·cos(bⁿπx) is continuous everywhere but differentiable… Continued Fractions — Best Rational ApproximationsNew📱Unfold any real number into continued fraction [a0; a1, a2,…] and watch convergents p/q… Spirograph — Hypotrochoids & EpitrochoidsNew📱Draw parametric rolling-circle curves: hypotrochoids trace inside a fixed ring, epitrochoids…