🟦 Wolfram 1D Cellular Automata
An elementary cellular automaton consists of a 1-D row of binary cells. Each cell's next state depends on itself and its two neighbours — 3 cells produce 2³=8 patterns, each mapping to 0 or 1, giving 2⁸ = 256 possible rules. Stephen Wolfram classified them into four classes: uniform, periodic, chaotic, and complex. Despite the simplicity, Rule 110 is Turing-complete (proven by Matthew Cook, 2004). Rule 30 is so unpredictable it is used as a random-number generator in Mathematica. Rule 90 produces the Sierpiński triangle. Type any rule number (0–255) or choose a famous preset.
Rule Number
Famous Rules
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Wolfram's Four Classes
Stephen Wolfram (in A New Kind of Science, 2002) classified cellular automata into four classes: Class I — converge to a uniform state (e.g. Rule 0, 255); Class II — periodic or stable structures (Rule 4, 108); Class III — chaotic, pseudo-random patterns (Rule 30); Class IV — complex, localised structures that persist — the most computationally interesting (Rule 110). The Rule 184 CA is a traffic flow model: 1s represent cars, showing jam formation above a critical density. The cone snail Conus textile bears a shell pattern that closely resembles Rule 30 — evolution found the same cellular automaton!