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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 ...
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 ...
More formally, the problem concerns cellular automata, arrays of finite-state machines called cells arranged in a line, such that at each time step each machine transitions to a new state as a function of its previous state and the states of its two neighbors in the line. For the firing squad problem, the line consists of a finite number of ...
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.
Any automaton of the above form that contains the element B1 (e.g. B17/S78, or B145/S34) will always be explosive for any finite pattern: at any step, consider the cell (x,y) that has minimum x-coordinate among cells that are on, and among such cells the one with minimum y-coordinate.
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]
A state of the Rule 184 automaton consists of a one-dimensional array of cells, each containing a binary value (0 or 1). In each step of its evolution, the Rule 184 automaton applies the following rule to each of the cells in the array, simultaneously for all cells, to determine the new state of the cell: [3]
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.