53 layers · 7 families

Pattern guide

Behind every layer of the generator is someone’s mathematics: Penrose tilings, the Gray–Scott model, the Mandelbrot set, Chladni plates. Each layer has its own page with a live demo: how it works, where it comes from and what to tweak.

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Tilings and mosaics

Tiles that cover the plane with no gaps or overlaps: from Archimedean lattices and girih to the aperiodic hat, plus knots and weaves.

⧉ SVG Archimedean tilings All 11 ways to tile the plane with regular polygons so that every vertex looks the same — and their duals, the Laves tilings.
⧉ SVG Islamic star patterns Girih by Hankin's method: rays leave the edge midpoints of an Archimedean tiling at one angle and meet as stars and rosettes, and the straps weave over and under.
SVG Quasiperiodic tilings Penrose, Ammann–Beenker and their relatives: order without repetition. De Bruijn's multigrid method and Robinson-triangle deflation.
SVG The aperiodic hat A single 13-sided tile that covers the plane yet never repeats (2023). Built by substituting the H, T, P and F metatiles.
⧉ SVG Truchet tiles One tile in random orientations builds endless paths and mazes.
⧉ SVG Maze A uniform spanning tree by Wilson's algorithm: exactly one path between any two cells. Seamless on a torus.
⧉ SVG Voronoi and Delaunay Every point claims the region closest to it: honeycombs, stained glass, low-poly mosaics. Bridson's Poisson disk and Lloyd relaxation.
⧉ SVG Circle packing Circles that grow until they touch fill the plane densely; the Apollonian gasket nests circles forever by Descartes' theorem.
⧉ SVG Celtic knots Knotwork on a Mercat grid: bands run diagonally, strictly over and under, and walls in the grid turn them back in smooth loops.
⧉ Weaves Cloth from a weave draft: plain, twill, satin, basket, herringbone, houndstooth and tartan — rounded threads dipping under each other.

Fields and noise

Continuous fields: Perlin and Worley noise, domain warping, wave interference and quasicrystals, the stuff of backgrounds and textures.

Simulations and growth

Patterns that grow by themselves: Turing’s chemistry, slime mould, cellular automata and leaf veins, computed step by step on the GPU.

Fractals

Self-similarity at every scale: the Mandelbrot set, fractal flames, strange attractors, the hyperbolic plane and L-systems.

Curves

Lines from formulas: banknote guilloche, the harmonograph, sunflower phyllotaxis, the superformula, streamlines and the ridgelines of Unknown Pleasures.

Sound

Patterns made of sound: a track’s spectrogram and chromagram, the XY oscilloscope, Chladni figures and Faraday waves from notes.

Effects

Processing everything below: the 17 wallpaper groups, kaleidoscope, halftone, dithering, relief, glow and grain.