Mercyhurst UniversityMath DeptDr Williams Home

One Line Automaton

About Elementary Cellular Automata

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 SierpiƄski triangle from a single starting cell.

Using the Applet

A rule can be entered in one of two ways: by entering the base 10 name of the rule (an integer between 0 and 255), or by clicking on the highlighted cells beneath each triple to toggle values in the binary string.

To enter a starting sequence, click the highlighted cells along the top row. Or, click the Random Condition button to generate a

About this Applet

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