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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 ...
A cellular automaton (CA) is a discrete dynamical system consisting of a uniform (finite or infinite) grid of cells. Each cell can be in only one of a finite number of states at a discrete time.
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.
In particular, the following are features of models of quantum cellular automata: The computation is considered to come about by parallel operation of multiple computing devices, or cells. The cells are usually taken to be identical, finite-dimensional quantum systems (e.g. each cell is a qubit). Each cell has a neighborhood of other cells.
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]
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.
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 (with different partitions at different time steps) and the transition rule is applied to a whole block at a time rather than a single cell. Block cellular automata are useful ...