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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]
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.
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 ...
For one-dimensional cellular automata, Gardens of Eden can be found by an efficient algorithm whose running time is polynomial in the size of the rule table of the automaton. For higher dimensions, determining whether a Garden of Eden exists is an undecidable problem , meaning that there is no algorithm that can be guaranteed to terminate and ...
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.
Hashlife is a memoized algorithm for computing the long-term fate of a given starting configuration in Conway's Game of Life and related cellular automata, much more quickly than would be possible using alternative algorithms that simulate each time step of each cell of the automaton. The algorithm was first described by Bill Gosper in the ...
In cellular automata, the von Neumann neighborhood (or 4-neighborhood) is classically defined on a two-dimensional square lattice and is composed of a central cell and its four adjacent cells. [1] The neighborhood is named after John von Neumann , who used it to define the von Neumann cellular automaton and the von Neumann universal constructor ...
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.