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The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, 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 configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine.
A cellular automaton 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. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling.
Highlife is a cellular automaton similar to Conway's Game of Life. It was devised in 1994 by Nathan Thompson. It is a two-dimensional, two-state cellular automaton in the "Life family" and is described by the rule B36/S23; that is, a cell is born if it has 3 or 6 neighbors and survives if it has 2 or 3 neighbors. Because the rules of HighLife and Conway's Life are similar, many simple patterns in Conway's Life function identically in HighLife. More complicated engineered patterns for one rule, though, typically do not work in the other rule.
In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position. The smallest such number of generations is called the period of the spaceship.
In a cellular automaton, a puffer train, or simply puffer, is a finite pattern that moves itself across the "universe", leaving debris behind. Thus a pattern consisting of only a puffer will grow arbitrarily large over time. While both puffers and spaceships have periods and speeds, unlike puffers, spaceships do not leave debris behind.
A cellular automaton (CA) is Life-like if it meets the following criteria:
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of an infinite two-dimensional grid of cells, each of which may be in one of two states: on or off. Each cell is considered to have eight neighbors, as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule B2/S.
The glider is a pattern that travels across the board in Conway's Game of Life. It was first discovered by Richard K. Guy in 1969, while John Conway's group was attempting to track the evolution of the R-pentomino. Gliders are the smallest spaceships, and they travel diagonally at a speed of one cell every four generations, or . The glider is often produced from randomly generated starting configurations.
In a cellular automaton, a gun is a pattern with a main part that repeats periodically, like an oscillator, and that also periodically emits spaceships. There are then two periods that may be considered: the period of the spaceship output, and the period of the gun itself, which is necessarily a multiple of the spaceship output's period. A gun whose period is larger than the period of the output is a pseudoperiod gun.
A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks and the transition rule is applied to a whole block at a time rather than a single cell. Block cellular automata are useful for simulations of physical quantities, because it is straightforward to choose transition rules that obey physical constraints such as reversibility and conservation laws.
In Conway's Game of Life and other cellular automata, a still life is a pattern that does not change from one generation to the next. The term comes from the art world where a still life painting or photograph depicts an inanimate scene. In cellular automata, a still life can be thought of as an oscillator with unit period.
A cyclic cellular automaton is a kind of cellular automaton rule developed by David Griffeath and studied by several other cellular automaton researchers. In this system, each cell remains unchanged until some neighboring cell has a modular value exactly one unit larger than that of the cell itself, at which point it copies its neighbor's value. One-dimensional cyclic cellular automata can be interpreted as systems of interacting particles, while cyclic cellular automata in higher dimensions exhibit complex spiraling behavior.
A rake, in the lexicon of cellular automata, is a type of puffer train, which is an automaton that leaves behind a trail of debris. In the case of a rake, however, the debris left behind is a stream of spaceships, which are automata that "travel" by looping through a short series of iterations and end up in a new location after each cycle returns to the original configuration.
In cellular automata such as Conway's Game of Life, a reflector is a pattern that can interact with a spaceship to change its direction of motion, without damage to the reflector pattern. In Life, many oscillators can reflect the glider; there also exist stable reflectors composed of still life patterns that, when they interact with a glider, reflect the glider and return to their stable state.
Rule 184 is a one-dimensional binary cellular automaton rule, notable for solving the majority problem as well as for its ability to simultaneously describe several, seemingly quite different, particle systems:
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.
Brian's Brain is a cellular automaton devised by Brian Silverman, which is very similar to his Seeds rule.
Life without Death is a cellular automaton, similar to Conway's Game of Life and other Life-like cellular automaton rules. In this cellular automaton, an initial seed pattern grows according to the same rule as in Conway's Game of Life; however, unlike Life, patterns never shrink. The rule was originally considered by Toffoli & Margolus (1987), who called it "Inkspot"; it has also been called "Flakes". In contrast to the more complex patterns that exist within Conway's Game of Life, Life without Death commonly features still life patterns, in which no change occurs, and ladder patterns, that grow in a straight line.
In Conway's Game of Life and related cellular automata, a spacefiller is a pattern that spreads out indefinitely, eventually filling the entire space with a still life pattern. It typically consists of three components: stretchers that resemble spaceships at the four corners of the pattern, a growing boundary region along the edges of the pattern, and the still life in the interior pattern.
Critters is a reversible block cellular automaton with similar dynamics to Conway's Game of Life, first described by Tommaso Toffoli and Norman Margolus in 1987.
References
- ↑ Gardner, Martin (October 1970). "Mathematical Games: The fantastic combinations of John Conway's new solitaire game "Life"". Scientific American. 223: 120–123.
- ↑ "Spaceship Speed Limits in "B3" Life-Like Cellular Automata". Nathaniel Johnston. 2009-10-30. Retrieved 2022-05-11.
- ↑ Nivasch, Gabriel. "Lightspeed signals in life". Archived from the original on 2002-12-11. Retrieved 2008-11-29.
- ↑ "Star Gate - from Eric Weisstein's Treasure Trove of Life C.A." Retrieved 2008-11-29.