five simple rules, grown live into five worlds
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Rule 110. An elementary 1D automaton (Wolfram). Each cell's next state is a fixed function of itself and its two neighbors — eight cases, three bits, and that table is the whole program. Yet Cook (2004) proved it Turing-complete: with the right starting row it can run any computation.
mechanism The three-cell neighborhood (left, center, right) indexes an 8-bit table — 110 is 01101110 — giving the next state. Applied to every cell each generation with toroidal wrap, run on the CPU where the rule reads as exactly what it is.
built Each generation is one row, stamped into a 2D texture that scrolls upward — a space-time diagram, vertical axis = time. Genesis is a single live cell (its sparse apex burned in so the screen fills); the newest third warms toward amber, the live computing edge. Its history seeds the next scene.
pointer Move over the field to drop a cluster of live cells — a fresh cascade nucleates and grows up the screen.
Game of Life. Conway (1970), rule B3/S23 — a dead cell with exactly three live neighbors is born, a live cell with two or three survives, all else dies. Deterministic, yet you cannot know a pattern's fate without running it; the Game is Turing-complete.
mechanism B3/S23 over the eight surrounding (Moore) neighbors on a toroidal grid, run entirely on the GPU — state in a float ping-pong buffer, one texel per cell, nearest-filtered so the cells stay crisp.
built Seeded from Rule 110's history over a sparse random soup (so the colony stays alive) — logic becomes life (the VOID → LIFE handoff). A heat channel leaves a fading cyan afterglow so the motion reads.
pointer Move across the grid to paint living cells into the colony.
Boids. Reynolds (1987) — three local urges: keep your distance, match your neighbors' heading, drift toward their center. No leader, no choreography — the murmuration's shape lives in the coupling between birds, not in any one of them.
mechanism Each agent couples to its ~7 nearest neighbors — topological, not a fixed radius (Ballerini et al., 2008); that fixed-few coupling is what forms the moving shapes instead of a blob. Up to ~16k agents, steered on the GPU via a spatial grid.
built A soft spherical boundary keeps it framed (Reynolds' 1999 "containment"), with a touch of damping that only bleeds off runaway energy — it never settles the flock. The flock arrives from LIFE — the cells you watched detach become these birds: a real state handoff, not a crossfade.
pointer Move through the flock to carve a vortex — it opens around you and curls past (the predator).
Gray-Scott. Reaction-diffusion — two chemicals diffuse at different rates and react, U + 2V → 3V, while V is removed. From a nearly uniform soup, spots, stripes and dividing cells precipitate: structure with no blueprint (Pearson, Science 1993).
mechanism Two coupled equations per cell — U' = Du·∇²U − U·V² + F(1−U), V' = Dv·∇²V + U·V² − (F+K)·V — with feed 0.055, kill 0.062. A fragment shader on a double FBO, many substeps a frame on the GPU.
built The boids fly in and stamp their footprint into the V field — the flock's motion seeds the chemistry (FLOCK → PATTERN). The field is read back to seed the mind that follows.
pointer Move over the field to inject activator — new growth blooms where you go.
Self-organizing map. Kohonen (1982) — a 2D lattice of nodes learns to drape a form. No node is told where to go; order emerges from local competition as the net lowers its own representation error.
mechanism Repeatedly: draw a sample, find the best-matching node, pull it and its grid-neighbors toward it — by a rate (α) and over a radius (σ) that both shrink with time. From a tangle the sheet unfolds, neighbors staying neighbors. CPU-computed: cyan nodes, violet edges.
built The reaction-diffusion pattern is the input distribution — the chemistry becomes the form the mind learns; the net condenses onto it as the pattern dissolves (PATTERN → MIND). Nodes flare as they win samples — neurons firing.
pointer The net reaches toward your cursor and parts into a crater around it.
00 — VOID. Rule 110, a Turing-complete cellular automaton: computation needs almost nothing to begin.
01 — LIFE. Conway's Game of Life: deterministic is not the same as predictable.
02 — FLOCK. Reynolds boids: the flock is a property no single bird contains.
03 — PATTERN. Gray-Scott reaction-diffusion: form, growing without a blueprint.
04 — MIND. A self-organizing map: order is a structure minimizing its own representation error.