📐 Mathematics

Penrose Tiling — Quasi-Periodic PatternsNew📱Generate Penrose P3 (thick and thin rhombus) tilings via deflation substitution. These… Eigenvalues — Linear Transformations & Principal AxesNew📱Edit a 2x2 matrix and watch it transform the unit circle into an ellipse: eigenvectors point… Hypocycloids & Epicycloids — Rolling Circle CurvesNew📱Watch a circle roll inside or outside a fixed circle and trace roulette curves — deltoid,… Newton's Method Fractal — Basins of AttractionNew📱Each pixel iterates Newton's method in ℂ toward a root, colored by which root it reaches.… Rose Curves — Rhodonea r = a·cos(kθ)New📱Draw rose curves r = a·cos(kθ) in polar coordinates. Set k = n/d, watch the parity rule… 3D Lissajous Curves — Harmonic KnotsNew📱Three perpendicular oscillators woven into a 3D Lissajous curve. Tune frequencies a:b:c and… Riemann Zeta Function — Critical Strip & ZerosNew📱Visualise the Riemann zeta function on the complex plane: domain-colour ζ(s), walk the… Origami Fold MathematicsNew📱Explore the mathematics of paper folding — crease patterns, fold sequences and rigid origami… Taylor Series — Polynomial ApproximationNew📱Visualise how Maclaurin polynomials approximate sin(x), cos(x) and eˣ. Slide N from 1 to 20… Eigenvalues & Eigenvectors — Linear Transformation VisualiserNew📱Interactive 2×2 matrix transformation visualiser. Drag matrix entries to see how… SVD CompressionNew📱Keep only the top k singular values of an image and watch how few rank-1 layers are needed… Space-Filling CurvesNew📱Watch Hilbert, Peano and Morton (Z-order) curves fill the plane. Colour by path position to… Ulam SpiralNew📱Lay the integers on a square spiral and mark the primes — striking diagonal patterns emerge.… Fourier Epicycles: Rotating Circle ChainsNew📱Explore the relationship between geometric shapes and oscillating waves as you draw a closed… Mandelbulb 3D FractalNew📱Explore the mesmerizing geometry of the Mandelbrot set and its associated fractal – the… Harmonograph: Pendulum Wave PatternsNew📱Explore how two swinging pendulums create mesmerizing, repeating patterns by adjusting their… Eigenvectors & Eigenvalues — Interactive Linear Algebra Visualizer📱Adjust 4 matrix entries and instantly see characteristic polynomial, eigenvalues λ₁ λ₂,… Torus & Genus — Topology Euler Characteristic Interactive📱Genus 0–3 surfaces (sphere, torus, double-torus, triple-torus). χ = V−E+F. Gauss-Bonnet… Diffusion-Limited Aggregation Fractal Growth📱Observe how particles spontaneously clump together in a fractal pattern as they randomly… Phase Portrait📱Tune the parameters of a 2D dynamical system and watch trajectories in the vector field… Reaction-Diffusion Patterns in a Turing System📱Explore how patterns emerge and evolve within a reaction-diffusion system by adjusting feed… Möbius Strip — Topology One-Sided Surface📱Trace a path along a Mobius strip to prove it has one side and one edge, then cut it… Newton's Fractal📱Newton's method applied to z^n − 1 = 0 in the complex plane. Each pixel is coloured by which… Sand Pile Model📱Bak–Tang–Wiesenfeld self-organised criticality. Drop grains of sand onto a grid; cells with… Complex Functions📱Domain coloring of complex functions. Hue encodes the argument and brightness encodes the… DFT & STFT Visualiser📱Generate signals and watch their Fourier transforms live. Switch between DFT magnitude… Riemann Integral Visualizer📱Witness the dramatic buildup and explosive release of a volcano, modeled using the… The 3n+1 Rule: Exploring the Collatz Conjecture📱Observe the iterative process of the 3n+1 rule as you input a starting number and watch its… Matrix Transformations — 2D Linear Algebra Visualizer📱Type a 2x2 matrix and watch the plane rotate, shear or scale, with the determinant as area… Klein Bottle — Topology of Non-Orientable Surfaces📱Rotate an immersed Klein bottle, follow its self-intersection, and see how two Mobius strips… Torus & Surface Genus — Topology of Orientable Surfaces📱Compare a sphere, torus and double torus by genus and Euler characteristic, and see how a… Knot Theory — Invariants, Crossings & Reidemeister Moves📱Deform a trefoil or figure-eight knot with Reidemeister moves and watch crossing number,… Fourier Series Interactive Phasor & Harmonic Decomposition📱Build waveforms from sine harmonics interactively. Watch rotating phasors trace square,… Sieve of Eratosthenes — Animated Prime Number Finder📱Watch the Sieve of Eratosthenes animate in real time. Cross off multiples of each prime and… Geodesic Domes📱Interactive 3D geodesic dome builder. Subdivide icosahedra, octahedra and tetrahedra at… Spherical Projections📱Compare Mercator, Mollweide, Lambert azimuthal equal-area, sinusoidal and equirectangular… Chaotic Fern Iteration System📱Explore the mesmerizing growth of a Barnsley fern through an iterative function system,… Voronoi Diagram📱Interactive Voronoi tessellation with Lloyd's algorithm for centroidal relaxation. Choose… Kaleidoscope: Infinite Symmetry Art📱Explore the mesmerizing world of infinite symmetry by manipulating folding parameters and… Pythagoras Tree📱A recursive fractal tree built from the Pythagorean theorem. Adjust branch angle, depth and… Parametric Spirograph Patterns📱Explore intricate spirograph patterns by adjusting the radii of two concentric circles and… Number Spirals📱Ulam spiral (prime diagonals), Sacks spiral, Fibonacci sunflower and composite highlight… Sierpiński Triangle📱Two methods: Chaos Game (random vertex jumps) and recursive subdivision. Hausdorff dimension… 1D Cellular Automata — Wolfram📱Explore all 256 Wolfram elementary cellular automaton rules. Watch Rule 30, 90, 110 and 184… Eigenvalues & Eigenvectors📱Interactive 2D matrix visualizer: watch the unit circle transform into an ellipse,… SVD Visualizer📱Watch a 2x2 matrix decompose as A=UΣVᵀ: rotate, stretch by singular values, then rotate… Fourier Series Decomposition📱Explore the breakdown of complex waveforms into simpler sinusoidal components using the… Wind Farm: A Riemann Integral Simulation📱Observe how kinetic energy is converted into electricity by a wind farm, visualized through… Fractal Explorer (2D)📱Zoom and pan a canvas-based Mandelbrot and Julia set explorer with adjustable iteration… Knot Diagram Explorer (2D)📱Rotate a projected trefoil or figure-eight knot to see how the drawn crossing count shifts… L-System Plant Growth (2D)📱A 2D canvas L-system engine: an axiom string is rewritten by grammar rules over several…