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Rule 30 is an elementary cellular automaton introduced by Stephen Wolfram in 1983. [2] 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.
Examples are rules 4, 108, 218 and 250. Class 3: Cellular automata which appear to remain in a random state. Examples are rules 22, 30, 126, 150, 182. Class 4: Cellular automata which form areas of repetitive or stable states, but also form structures that interact with each other in complicated ways. An example is rule 110.
The rule 30, rule 90, rule 110, and rule 184 cellular automata are particularly interesting. The images below show the history of rules 30 and 110 when the starting configuration consists of a 1 (at the top of each image) surrounded by 0s.
Langton's ant can also be described as a cellular automaton, where the grid is colored black or white and the "ant" square has one of eight different colors assigned to encode the combination of black/white state and the current direction of motion of the ant.
Cellular automata on a two-dimensional grid that can be described in this way are known as Life-like cellular automata. Another common Life-like automaton, Highlife , is described by the rule B36/S23, because having six neighbours, in addition to the original game's B3/S23 rule, causes a birth.
A code of this type suffixed by an R, such as "Rule 37R", indicates a second-order cellular automaton with the same neighborhood structure. While in a strict sense every Wolfram code in the valid range defines a different rule, some of these rules are isomorphic and usually considered equivalent. For example, rule 110 above is isomorphic with ...
For instance, in this notation, Conway's Game of Life is denoted 23/3. [2] [3] In the notation used by the Golly open-source cellular automaton package and in the RLE format for storing cellular automaton patterns, a rule is written in the form By/Sx where x and y are the same as in the MCell notation. Thus, in this notation, Conway's Game of ...
The Rule 110 cellular automaton (often called simply Rule 110) [a] is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. [2]