About This Tool
The 1D Cellular Automaton visualizer lets you explore all 256 elementary rules defined by Stephen Wolfram. Starting from a single center cell, each rule produces a new row every tick by looking at every cell and its two neighbours. The patterns range from simple repetition to fractal triangles to provably Turing-complete computation — all from a one-bit, three-cell neighbourhood.
How to Use
Watch the default Rule 110 draw itself row by row from a single center cell.
Click a preset (30, 90, 110, 184) to instantly switch rules and restart.
Type any number from 0 to 255 in the Custom field to explore other rules.
Use the Speed buttons to slow down and study the pattern or speed up to fill the canvas faster.
Hit Reset to restart the current rule from the center seed.
Frequently Asked Questions
What is an elementary cellular automaton?
It is a 1D grid of cells that are either on or off. Each generation, every cell looks at itself and its two neighbours (8 possible patterns) and applies a fixed rule to decide its next state. There are exactly 256 such rules, numbered 0–255 by Stephen Wolfram.
Why is Rule 110 special?
Rule 110 is mathematically proven to be Turing-complete, meaning it can in principle simulate any computation given the right initial conditions. It was proven by Matthew Cook in 2004.
What does Rule 30 generate?
Rule 30 produces chaotic, apparently random output from a simple deterministic rule. Wolfram used it as the basis for the random number generator in Mathematica.
Why does Rule 90 look like a triangle?
Rule 90 is equivalent to XOR of the two neighbours, which naturally generates the Sierpiński triangle — a self-similar fractal that appears at every scale.
Can I enter any rule number?
Yes — type any integer from 0 to 255 in the Custom field. Each number encodes a unique set of outputs for the 8 possible neighbourhood patterns, giving 256 distinct rules to explore.