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All the 256 elementary cellular automaton rules [1] (click or tap to enlarge). In mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current ...
The number of possible rules, R, for a generalized cellular automaton in which each cell may assume one of S states as determined by a neighborhood size of n, in a D-dimensional space is given by: R=S S (2n+1) D. The most common example has S = 2, n = 1 and D = 1, giving R = 256. The number of possible rules has an extreme dependence on the ...
Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been directly proven, although proofs for several similar rules follow as simple corollaries (e.g. Rule 124, which is the horizontal reflection of Rule 110). Rule 110 is arguably the simplest known Turing complete system.
An animation of the way the rules of a 1D cellular automaton determine the next generation. These 256 cellular automata are generally referred to by their Wolfram code, a standard naming convention invented by Wolfram that gives each rule a number from 0 to 255. A number of papers have analyzed and compared the distinct cases among the 256 ...
Print/export Download as PDF; Printable version; ... Pages in category "Cellular automaton rules" The following 33 pages are in this category, out of 33 total.
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.
Gács, Kurdyumov, and Levin found an automaton that, although it does not always solve the majority problem correctly, does so in many cases. [1] In their approach to the problem, the quality of a cellular automaton rule is measured by the fraction of the + possible starting configurations that it correctly classifies.
Technically, they are not cellular automata at all, because the underlying "space" is the continuous Euclidean plane R 2, not the discrete lattice Z 2. They have been studied by Marcus Pivato. [24] Lenia is a family of continuous cellular automata created by Bert Wang-Chak Chan. The space, time and states of the Game of Life are generalized to ...