All models

MathPets source

Wolfram Automaton

1D cellular rulesrow-by-row historyrule selectionflip errorsdependency coloringwrap-x topology
Open in VS Code

Elementary cellular automata were popularized by Stephen Wolfram in the 1980s as a minimal laboratory for computation and complexity. A single row of binary cells can produce repetition, randomness, nested structure, and famous rules such as Rule 30.

This model treats the board as a history sheet. Setup seeds the top row with either one central live cell or a random-density row controlled by the cell density slider, then each tick reads left, center, and right cells from the current source row, uses the selected 0-255 rule number to decide the next row, and moves downward until the board is filled. Horizontal wrapping keeps the one-dimensional world continuous.

The error probability slider decides whether each generated row gets one flipped cell. Flip sources start red, and every later cell whose neighborhood depends on an affected parent inherits that error event's color from a scale, so separate causal cones remain visually distinct.

board · 920 × 920grid · on