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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 ...
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] Cellular automata have found application in various ...
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 ...
The fumarole, a period-5 oscillator in Conway's Game of Life.The two live cells appearing at the top of the pattern every five generations are considered a spark. In Conway's Game of Life and similar cellular automaton rules, a spark is a small collection of live cells that appears at the edge of some larger pattern such as a spaceship or oscillator, then quickly dies off.
A sample autonomous pattern from Lenia. An animation showing the movement of a glider in Lenia. Lenia is a family of cellular automata created by Bert Wang-Chak Chan. [1] [2] [3] It is intended to be a continuous generalization of Conway's Game of Life, with continuous states, space and time.
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 ...
The first known puffer, in Conway's Game of Life, was discovered by Bill Gosper; it is a dirty puffer, but eventually stabilizes to leave a pattern of debris that repeats every 140 generations. [1] Since then, many puffers have been discovered for this cellular automaton, with many different speeds and periods. [2]
Conway came to dislike how discussions of him heavily focused on his Game of Life, feeling that it overshadowed deeper and more important things he had done, although he remained proud of his work on it. [26] The game helped to launch a new branch of mathematics, the field of cellular automata. [27] The Game of Life is known to be Turing complete.