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In von Neumann's cellular automaton, the finite state machines (or cells) are arranged in a two-dimensional Cartesian grid, and interface with the surrounding four cells. As von Neumann's cellular automaton was the first example to use this arrangement, it is known as the von Neumann neighbourhood. The set of FSAs define a cell space of ...
The array of cells of the automaton has two dimensions. Each cell of the automaton has two states (conventionally referred to as "alive" and "dead", or alternatively "on" and "off") The neighborhood of each cell is the Moore neighborhood; it consists of the eight adjacent cells to the one under consideration and (possibly) the cell itself.
A cellular automaton is a type of model studied in mathematics and theoretical biology consisting of a regular grid of cells, each in one of a finite number of states, such as "on" and "off". A pattern in the Life without Death cellular automaton consists of an infinite two-dimensional grid of cells, each of which can be in one of two states ...
Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions.
A cellular automaton is defined by its cells (often a one- or two-dimensional array), a finite set of values or states that can go into each cell, a neighborhood associating each cell with a finite set of nearby cells, and an update rule according to which the values of all cells are updated, simultaneously, as a function of the values of their neighboring cells.
Cellular automata were used in the early days of artificial life, and are still often used for ease of scalability and parallelization. Alife and cellular automata share a closely tied history. Artificial neural networks are sometimes used to model the brain of an agent.
As in a typical two dimensional cellular automaton, [1] consider a rectangular grid, or checkerboard pattern, of "cells". It can be finite or infinite in extent. Each cell has a set of "neighbors". In the simplest case, each cell has four neighbors, those being the cells directly above or below or to the left or right of the given cell. [2]
In all of Wolfram's elementary cellular automata, an infinite one-dimensional array of cellular automaton cells with only two states is considered, with each cell in some initial state. At discrete time intervals, every cell spontaneously changes state based on its current state and the state of its two neighbors.