Computation & Complexity
Wolfram Elementary Automata
An elementary cellular automaton is a 1D row of cells, each black or white. At each time step, every cell updates based on itself and its two neighbors — 8 possible neighborhood patterns, giving 2⁸ = 256 distinct rules. Despite their simplicity, some rules produce fractals, randomness, and even universal computation (Rule 110).
30
Rule table (neighborhood → output)
Rule number (0–255)
Cell size (px)
3
Initial state
Color
Class
—
Total rules
256 (2⁸ neighborhoods × binary output)
Rule 110
Proved Turing-complete by Matthew Cook (2004)
Rule 30
Used in Mathematica's random number generator