Elementary Cellular Automata
Explore all 256 Wolfram elementary cellular automata. Scrub the rule, seed from a single cell or randomness, recolour and export — see Rule 30, 90, 110 emerge.
Rule 30 = 00011110₂
What is an elementary cellular automaton?
It's the simplest interesting computer there is: a row of cells, each on or off. Every step, a cell's next state depends only on itself and its two neighbours. Three binary inputs give 8 possible neighbourhoods; choosing an output (0/1) for each of those 8 cases is an 8-bit number — a “rule” from 0 to 255 (the Wolfram code). Each row below is one time step; time runs downward.
Despite trivial rules, the behaviour is anything but. This is the textbook example of emergence: complexity with no designer.
Rules worth seeing
- Rule 90: draws the Sierpiński triangle — a fractal from a single cell.
- Rule 30: chaotic and statistically random — Wolfram used it as a random-number generator in Mathematica.
- Rule 110: proven Turing-complete — it can, in principle, compute anything a computer can.
- Rule 184: a minimal traffic-flow model; Rule 54 sits on the edge of chaos with travelling particles.
Wolfram's four classes
I — Homogeneous
Everything dies or freezes to a single state (e.g. Rule 0, 255).II — Periodic
Settles into stable or repeating stripes and structures.III — Chaotic
Aperiodic, random-looking texture (Rule 30, 45, 90 from random seeds).IV — Complex
Localized structures that move and interact (Rule 110, 54) — where computation lives.Single cell vs random seed
Starting from one cell reveals a rule's pure geometry — fractals and triangles grow from that seed. Starting from a random row shows its bulk dynamics — which patterns survive, merge or annihilate. The legend under the canvas shows the rule's 8-bit transition table: top squares are the three-cell neighbourhood, the square below is the resulting state for the current rule.