Search results
Results from the WOW.Com Content Network
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 ...
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 ...
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 ...
Langton's ant is a two-dimensional Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. [1] The idea has been generalized in several different ways, such as turmites which add more colors and more states.
Mirek's Cellebration is a freeware one- and two-dimensional cellular automata viewer, explorer, and editor for Windows. It includes powerful facilities for simulating and viewing a wide variety of cellular automaton rules, including the Game of Life, and a scriptable editor. Xlife is a cellular-automaton laboratory by Jon Bennett.
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.
big.assets.huffingtonpost.com
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.