Search results
Results from the WOW.Com Content Network
The simplest nontrivial cellular automaton would be one-dimensional, with two possible states per cell, and a cell's neighbors defined as the adjacent cells on either side of it. A cell and its two neighbors form a neighborhood of 3 cells, so there are 2 3 = 8 possible patterns for a neighborhood. A rule consists of deciding, for each pattern ...
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 ...
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman [1] [2] and named by Mirek Wójtowicz. [1] [3] 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 (Moore neighborhood), as in ...
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 mathematics and computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors.
The rule for the automaton within each of these subsets is equivalent (except for a shift by half a cell per time step) to another elementary cellular automaton, Rule 102, in which the new state of each cell is the exclusive or of its old state and its right neighbor. That is, the behavior of Rule 90 is essentially the same as the behavior 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.
If we view the two states as Boolean values, this correspondence between ordinary and second-order automaton can be described simply: the state of a cell of the second-order automaton at time t + 1 is the exclusive or of its state at time t − 1 with the state that the ordinary cellular automaton rule would compute for it. [4]