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The Game of Life, also known as Conway's Game of Life or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. [1] It is a zero-player game, [2] [3] meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial ...
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.
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]
Gosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life [1] 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 ...
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.
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 ...
Time-space diagram of Rule 90 with random initial conditions. Each row of pixels is a configuration of the automaton; time progresses vertically from top to bottom. In the mathematical study of cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each ...
An immediate corollary is that an injective cellular automaton must be surjective. Moore proved one direction of the theorem, that automata with twins have orphans; [2] Myhill proved the converse, that an automaton with an orphan also has twins. [15] In the case of Conway's Game of Life, twins are much easier to find than orphans.