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 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.
A cellular automaton (CA) is Life-like if it meets the following criteria:
In a cellular automaton, a Garden of Eden is a configuration that has no predecessor. It can be the initial configuration of the automaton but cannot arise in any other way. John Tukey named these configurations after the Garden of Eden in Abrahamic religions, which was created out of nowhere.
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 cellular automata, the Moore neighborhood is defined on a two-dimensional square lattice and is composed of a central cell and the eight cells that surround it.
In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square on a chessboard and each edge is a legal move. More specifically, an king's graph is a king's graph of an chessboard. It is the map graph formed from the squares of a chessboard by making a vertex for each square and an edge for each two squares that share an edge or a corner. It can also be constructed as the strong product of two path graphs.
Wolfram code is a naming system often used for one-dimensional cellular automaton rules, introduced by Stephen Wolfram in a 1983 paper and used in his book A New Kind of Science.
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.
Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm", which will become the daughter loop. The "genes" instruct it to make three left turns, completing the loop, which then disconnects from its parent.
The idea of human artifacts being given life has fascinated humankind for as long as people have been recording their myths and stories. Whether Pygmalion or Frankenstein, humanity has been fascinated with the idea of artificial life.
John von Neumann's universal constructor is a self-replicating machine in a cellular automata (CA) environment. It was designed in the 1940s, without the use of a computer. The fundamental details of the machine were published in von Neumann's book Theory of Self-Reproducing Automata, completed in 1966 by Arthur W. Burks after von Neumann's death. While typically not as well-known as von Neumann's other work, it is regarded as foundational for automata theory, complex systems, and artificial life. Indeed, Nobel Laureate Sydney Brenner considered Von Neumann's work on self-reproducing automata central to biological theory as well, allowing us to "discipline our thoughts about machines, both natural and artificial."
Cellular automata, as with other multi-agent system models, usually treat time as discrete and state updates as occurring synchronously. The state of every cell in the model is updated together, before any of the new states influence other cells. In contrast, an asynchronous cellular automaton is able to update individual cells independently, in such a way that the new state of a cell affects the calculation of states in neighbouring cells.
A quantum cellular automaton (QCA) is an abstract model of quantum computation, devised in analogy to conventional models of cellular automata introduced by John von Neumann. The same name may also refer to quantum dot cellular automata, which are a proposed physical implementation of "classical" cellular automata by exploiting quantum mechanical phenomena. QCA have attracted a lot of attention as a result of its extremely small feature size and its ultra-low power consumption, making it one candidate for replacing CMOS technology.
In mathematics, a Delannoy number describes the number of paths from the southwest corner of a rectangular grid to the northeast corner, using only single steps north, northeast, or east. The Delannoy numbers are named after French army officer and amateur mathematician Henri Delannoy.
The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund credited Curtis and Lyndon as co-discoverers. It has been called "one of the fundamental results in symbolic dynamics".
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.
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor. That is, it is a regular grid of cells, each containing a state drawn from a finite set of states, with a rule for updating all cells simultaneously based on the states of their neighbors, such that the previous state of any cell before an update can be determined uniquely from the updated states of all the cells. The time-reversed dynamics of a reversible cellular automaton can always be described by another cellular automaton rule, possibly on a much larger neighborhood.
A cellular evolutionary algorithm (cEA) is a kind of evolutionary algorithm (EA) in which individuals cannot mate arbitrarily, but every one interacts with its closer neighbors on which a basic EA is applied.
In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few active neighbors are successively removed from the active set until the system stabilizes. The order in which this removal occurs makes no difference to the final stable state.
