1-dimension Cellular Automata

Neighborhood Rules

(click on the buttons to change the output)

Wrap

This is a JavaScript implementation of a cellular automaton, a type of algorithm where "cells" change state according to given rules. In particular, this example is a two-state, one-dimensional automaton.
It has been called the Elementary Cellular Automaton by Stephen Wolfram, who studied this type of automata.
In this program, we consider a one-dimensional space of cells that can only have one of two states - here, "black" or "white". Each automaton is defined by a set of "rules" which specify, for each cell, the next state of the cell, depending on its own current state and that of its two neighbours.
Despite the apparent simplicity of the algorithm, some rules can provide interisting results. Notably, Rule 110 has been proved to have the property of universality.
On this page, you may run a cellular automaton, defining the neighboorhood rules and whether to use a simple initial condition (I.C.) of only one black pixel, or a random I.C.

Some rules:

(Note: most rules produce more impressive results with "Simple I.C.")

Class 1 (Uniform)

Rule 254: Uniform black triangle

Class 2 (Pattern)

Rule 50: Checkerboard
Rules 57 and 99: "Pyramid"
Rules 62 and 118
Rule 73
Rules 190 and 246: Diagonal lines

Class 3 (Random)

Rules 30 and 86
Rules 60 and 102: Leaning Sierpiński
Rules 75 and 89
Rule 90: Sierpiński triangle
Rule 105
Rule 150

Class 4 (Complex)

Rules 110 and 124
Rules 169 and 225