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Class 1: Cellular automata which rapidly converge to a uniform state. Examples are rules 0, 32, 160 and 232. Class 2: Cellular automata which rapidly converge to a repetitive or stable state. 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.
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. [2]
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 .
The collection of all possible states of a cellular automaton over a group can be described as the functions that map each group element to one of the symbols in the alphabet. As a finite set, the alphabet has a discrete topology , and the collection of states can be given the product topology (called a prodiscrete topology because it is the ...
Pages in category "Cellular automaton rules" The following 33 pages are in this category, out of 33 total. This list may not reflect recent changes. 0–9. 3D Life; A.
A cellular automaton is defined by its cells (often a one- or two-dimensional array), a finite set of values or states that can go into each cell, a neighborhood associating each cell with a finite set of nearby cells, and an update rule according to which the values of all cells are updated, simultaneously, as a function of the values of their neighboring cells.
In von Neumann's cellular automaton, the finite state machines (or cells) are arranged in a two-dimensional Cartesian grid, and interface with the surrounding four cells. As von Neumann's cellular automaton was the first example to use this arrangement, it is known as the von Neumann neighbourhood. The set of FSAs define a cell space of ...
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 ...