Elementary cellular automaton
Controls
Wolfram rule
Tape length
Number of generations
Description
Here is an interactive simulator of an elementary cellular automaton. On a one-dimensional tape, you create the initial configuration yourself: just click any cell to toggle it from inactive to active (and back). Choose an evolution rule (from 0 to 255), set the tape length and the desired number of generations - then start the process. Each new generation is calculated instantly according to the classic Wolfram rule and displayed in real time. A convenient way to observe how trivial local rules give rise to surprising global patterns - from stable structures to chaos.
General Information
An elementary cellular automaton is a one-dimensional tape, infinitely extended in both directions, in which each cell is in one of two states: 0 or 1. There is also a rule that determines the state of a cell at the next time step. To determine the next state of a cell, the rule uses the current state of that cell as well as the states of its two neighboring cells.
It can be observed that there are 2³ = 8 possible combinations of states for a cell and its two neighbors. The rule must specify the next state for each of these eight combinations. Therefore, there are altogether 2⁸ = 256 possible rules. Stephen Wolfram proposed a numbering system for these rules, now widely known as the Wolfram code. The essence of the Wolfram code is to write the possible combinations in descending order (111, 110, 101, 100, 011, 010, 001, 000), and below them write the corresponding output (next state) for each combination. The resulting string of 8 bits is then interpreted as a binary number, which becomes the rule number
Wolfram code example
| 111 | 110 | 101 | 100 | 011 | 010 | 001 | 000 |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |