In an elementary cellular automaton, each cell can appear in one of two possible states (depicted here as light and dark), with a rule determining the state of each cell based on its three northern neighbors. Each of the three neighbors can form one of eight possible sequences, ordered here according to the Wolfram Code as described by Stephen Wolfram in 1983. Each of these eight sequences can be set to result in one of two possible states; hence, there are a total of \(2^8=256\) possible rules. Each rule can be represented as a 8 digit binary string. The name of each rule is decided by the base 10 equivalent of this bit string.

Some rules are particularly interesting, including Rule 30 which is chaotic, Rule 54 which is believed to be universal, and Rule 90 which generates the Sierpiński triangle from a single starting cell.

Enter a rule (using its base ten value) in the text box, or change the rule by clicking the individual rules at the top of the applet. Change the starting state of first row by clicking the boxes. You can also generate a random starting state by clicking the Random State button. The sequence of generations will be displayed below the first row. Click the Save PNG button to save your automaton; the file name and image will include the rule used.

This applet was created using JavaScript and the Konva graphics library. It was last updated in March 2022.