ムクドリの群舞を設計する者はいません。どの細胞も、自分がヒョウの 斑紋の一部だとは知りません。格子に隣接セルについての一つのルールを与え、千羽の鳥に互いについての一つのルールを与え、脳を持たない粘菌に迷路を 解かせてみてください——すると構造がどこからともなく立ち現れます。これらは複雑性のおもちゃです。一行で読めるほど単純でありながら、いまだに予測できないほど奥深いのです。再生を押して、全体が部分を 超えていくさまをご覧ください。
A panicking crowd flees a room under Helbing's social-force model — watch arches clog the doorway, push the panic up and throughput drops (faster-is-slower), then drop a pillar by the door and flow climbs.
Four cell states and three rules build clocks, diodes and logic gates as electrons chase along copper wire.
A lattice of stubborn neighbours: each cell keeps borrowing a random neighbour’s opinion until coarsening domains slowly devour one another and the crowd lands on consensus — unless a few immovable zealots flip the whole population.
Thousands of self-propelled specks, each only copying its neighbours’ heading — dial down the noise and a leaderless flock crystallizes out of the swarm.
A 2D Turing machine with internal state on a grid of colours — a single head whose transition table conjures growing spirals, snowflakes, and fractal cities out of an empty lattice.
Hundreds of brainless termites blunder across a field of scattered wood chips — pick one up, carry it, drop it beside another — and with no blueprint, no foreman, and no memory, the litter slowly gathers itself into a handful of growing piles.
Scatter thousands of identical foragers over two sugar mountains, let each greedily walk to the richest patch it can see and pay its keep — and from a perfectly even start a steep order of rich and poor crystallises, the Gini coefficient climbing in real time while the Lorenz curve bows away from equality.
Reiter’s hexagonal cellular automaton grows the iconic six-fold snow crystal one diffusion step at a time — from a single frozen seed to a stellar dendrite.
Rafler's continuous-space Game of Life — Conway's rules melted onto a smooth [0,1] field, where soft gliders crawl and luminous blobs drift, merge and divide like living cells.
Give every agent on a checkerboard city the mildest of preferences — be content as long as merely a third of your neighbours share your colour — and watch a perfectly mixed grid tip, within a handful of steps, into stark blocks of one kind, the segregation index climbing toward total even though no one ever wanted it.
From one lit cell, the XOR rule draws the Sierpiński triangle — the very same fractal as Pascal’s triangle with the odd numbers shaded, then generalised mod 3, 5 and 7 by Lucas’ theorem.
A lattice of species locked in a cyclic food chain — each one hunted by the next — self-organises a random soup into chasing, rotating spiral waves.
On a single-lane ring with no bottleneck, a tiny hesitation snowballs into a stop-and-go wave that crawls backward against the flow — the jamiton, born from driver imperfection alone.
Open each lattice site with probability p, watch the clusters, and catch the instant a single giant component snaps across the grid at the critical threshold.
A two-state Turing machine on a grid: one ant, one rule per colour, and ten thousand steps of chaos that suddenly straightens into an endless highway.
A self-reproducing cellular automaton: one tiny loop carries an instruction tape, extends a construction arm, copies itself, and buds a growing colony of replicators — life-like reproduction from eight states and 219 rules.
A lattice of magnetic spins boiling between order and chaos — cool it past the Curie point and watch domains crystallize out of noise.
Gerhardt & Schuster’s excitable-medium cellular automaton: a random soup of sick and healthy cells spontaneously winds itself into rotating spiral and target waves — the same patterns the Belousov–Zhabotinsky reaction makes in a dish.
Trees grow, lightning strikes, fire sweeps — three cell rules that tune themselves to the edge of chaos, where blazes become scale-free.
A field of fireflies starts blinking in chaos; each one nudges its neighbours a little forward when it flashes, and out of nowhere the whole meadow locks into one breathing pulse.
The famous oscillating chemical reaction, simulated as an excitable medium — broken wavefronts curl into rotating blue↔red spirals and a stimulus blooms into concentric target waves.
A three-state excitable automaton that never sits still — firing cells leave dying wakes, spawning endless streams of self-propelled gliders.
Rain particles straight down onto a growing surface and watch three deposition rules carve three different roughnesses — uncorrelated, smoothed, and the rugged KPZ overhangs in between.
Self-propelled disks with nothing but rotational noise and a shove — crank the density and dense clumps condense out of a dilute gas with no attraction at all (MIPS).
0 から 255 までのたった一つのルール番号が、時間の無限のタペストリーを織りなすさまをご覧ください——カオス的なノイズから、フラクタルな秩序、そしてチューリング完全な計算まで。
制約伝播が、純粋な隣接ルールだけから回路・結び目・風景をタイルごとに織り上げるさまをご覧ください。
頭を持たない数十万のフィサルム・エージェントが化学的な跡を嗅ぎ取り、自然発生的に最適な輸送ネットワークへと配線されます。
一点に数百万の砂粒を落とし、崩落ルールが純粋な算術から完璧に自己相似なフラクタル曼荼羅を彫り出すさまをご覧ください。
二つの化学物質がトーラス状の格子上で追いかけ合い、互いを消費しながら、純粋な数学からサンゴの扇、ヒョウの斑紋、迷宮のような迷路を自然発生的に育てます。
小さなランダムなニューラルネットワークが各セルを統御します——成長し、自己修復し、異世界めいた生きたテクスチャへと花開くさまをご覧ください。
連続状態・連続カーネルのセルオートマトンで、なめらかなガウス畳み込みが生命なきノイズを、這い回り、分裂し、自己組織化するブロブへと誘い出します。
コンウェイのプレイヤー不在の宇宙——セルを描き、ルールを形づくり、グライダーやグライダー銃がカオスから構造を刻み出すさまをご覧ください。
純粋なブラウン運動のカオスから、フラクタルな稲妻の木が結晶化するさまをご覧ください——ガラスの霜、サンゴ礁、稲妻を彫り上げるのと同じルールです。
ランダムなピクセルのスープが、回転する渦巻き状の「デーモン」へと自己組織化するさまをご覧ください——ベロウソフ・ジャボチンスキー化学反応を駆動するのと同じ可励起媒質のダイナミクスです。
わずか三つの局所ルール——分離・整列・結合——から、数百の自律エージェントが自然発生的に群舞を形づくるさまをご覧ください。
数百匹の仮想アリが、フェロモンの跡だけを頼りに食料源を見つけて利用します——指導者もなく、地図もなく、あるのはスティグマジーだけです。