Rule 30

Rule 30 is a one-dimensional binary cellular automaton rule introduced by Stephen Wolfram in 1983. Using Wolfram's classification scheme, Rule 30 is a Class III rule, displaying aperiodic, chaotic behaviour.

This rule is of particular interest because it produces complex, seemingly random patterns from simple, well-defined rules. Because of this, Wolfram believes that Rule 30, and cellular automata in general, are the key to understanding how simple rules produce complex structures and behaviour in nature. For instance, a pattern resembling Rule 30 appears on the shell of the widespread cone snail species Conus textile. Rule 30 has also been used as a random number generator in Mathematica, and has also been proposed as a possible stream cipher for use in cryptography.

Rule 30 is so named because 30 is the smallest Wolfram code which describes its rule set (as described below). The mirror image, complement, and mirror complement of Rule 30 have Wolfram codes 86, 135, and 149, respectively.

In all of Wolfram's elementary cellular automata, an infinite one-dimensional array of cellular automaton cells with only two states is considered, with each cell in some initial state. At discrete time intervals, every cell spontaneously changes state based on its current state and the state of its two neighbors. For Rule 30, the rule set which governs the next state of the automaton is:

The following diagram shows the pattern created, with cells colored based on the previous state of their neighborhood. Darker colors represent "1" and lighter colors represent "0". Time increases down the vertical axis.

The following pattern emerges from an initial state in a single cell with state 1 (shown as black) is surrounded by cells with state 0 (white).

Rule 30 cellular automaton

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