Phenomena modelled
Patterns
Local rules that grow into shapes, fractals, and changing worlds.
Cellular automata, fractals and chaos: tiny rules, repeated, that produce far more structure than they seem to contain.
Models 18
18 models in this collection.
Cellular automataLife
What does a random soup of live cells settle into, and how long does it take?Conway's Game of Life on a 97 × 97 torus, started from a random 35% fill. Activity burns out over several hundred to a few thousand ticks, leaving still lifes, blinkers and gliders.
Physics & patternsTuring Diffusion
How much faster must U diffuse than V before the seed spreads instead of freezing?Gray–Scott reaction–diffusion: two fields, U and V, react and spread from a seeded square. By default narrow stripes grow out and cover the board; with slower diffusion the seed freezes into a ring.
Cellular automataFire
At what density does the fire cross the forest?Trees are planted at random, the trees in the left column are lit, and fire spreads to adjacent trees each tick. At 60% density it reaches the right edge in about half of runs.
Cellular automataLenia
How far can mu and sigma move before the glider dies or starts to multiply?Game of Life with continuous states, a ring-shaped kernel of radius 10 and a smooth growth function. The default seed settles into an Orbium glider that keeps crossing the 51 × 51 torus.
Chaos & fractalsMandelbrot & Julia Sets
What happens to a Julia set when its c moves outside the Mandelbrot set?Each patch is a point of the complex plane iterating z → z² + c, one step per tick. Points past |z| = 2 are colored by how fast they escaped; what remains at max-iterations is the Mandelbrot or Julia set.
Physics & patternsSandpile
How full does the pile get before losses at the edges balance the grains being added?Grains land on the center patch every tick. Any patch holding 4 or more passes one to each of its 4 neighbors, and grains pushed off the edge are lost, so the pile fills until the losses match the drip.
Physics & patternsPercolation
At what porosity does the water first reach the bottom?Water enters the open pores along the top of a random rock and wets every pore connected to them. It rarely reaches the bottom at porosity 55 and almost always does at 62.
Cellular automataLangton's Loops
How does an 86-cell loop with 8 possible cell states copy itself?Christopher Langton's 8-state self-reproducing loop. Signals circulating inside a sheathed loop build an arm, bend it into a copy of the loop and cut it free, every 151 ticks.
Cellular automataWolfram Automaton
Which rules turn a single live cell into a regular, a nested or an irregular pattern?An elementary cellular automaton drawn one generation per row, from one live cell at the top. rule picks any of the 256 rules (30 by default), and an occasional flipped cell colors the cone below it.
Cellular automataRule 110
What does a small disturbance in Rule 110's periodic background turn into?Elementary cellular automaton rule 110 on an 84-cell ring, drawn as a spacetime diagram. The default row is the periodic background (the ether) with one small disturbance, which becomes a glider.
Cellular automataWireworld
What happens to a clock's pulses when their wire runs into a thick block of conductor?Brian Silverman's four-state circuit automaton: electrons (blue head, red tail) move one cell per tick along yellow conductor. Three layouts: a clock feeding a wire, two clocks, and a random mesh.
Chaos & fractalsChaos Game
What shape do random half-way jumps toward three corners draw?Hidden walkers jump a fixed fraction of the way toward a randomly chosen corner and mark the patch they land on. With 3 corners and half-way jumps the marks trace a Sierpiński triangle.
Chaos & fractalsFractal Tree
How much of the board does the tree cover, and which setting controls that most?One walker paints a trunk up from the bottom of the board, then splits into two walkers turned ±branch-angle with shorter segments, and so on. At the defaults the tree has 64 tips after 46 ticks.
Chaos & fractalsLogistic Map
How many steps do two orbits that start 0.001 apart stay together?Two logistic-map orbits, x → r·x·(1 − x), start 0.001 apart and are plotted side by side, one column per tick. At r = 3.9 they separate within about 8 steps; at r = 3.2 they never do.
Cellular automataMaze
How do runners with no map and no memory still find the exit?A scent spreads from the exit through open corridors, weakening by a fixed factor per cell, and runners step toward the strongest neighboring scent. In the Labyrinth they reach the exit around tick 220.
Cellular automataHierarchical Cellular Automaton
Does a Life soup evolve differently when growing regions get looser birth and survival rules?Conway's Life on a 48 × 48 torus, with two coarser layers, 4 × 4 clusters and 12 × 12 districts, whose state is meant to loosen or tighten each cell's birth and survival rule.
Cellular automataLife Pet-Based
What starting density leaves the most cells alive once the soup settles down?Conway's Game of Life with one pet per cell instead of patch states, on a 41 × 41 torus. The rule is the same as in the patch version; only the representation changes.
Cellular automataConway 3D
How do Life dynamics change when moving from 8 neighbors in 2D to 26 neighbors in 3D?Three-dimensional Game of Life on an 8x8x8 cubic lattice rendered as a volume of unit voxels.