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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.
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.
Each cell is considered to have eight neighbors (Moore neighborhood), as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule B2/S. [1]
The number of live cells per generation of the pattern shown above demonstrating the monotonic nature of Life without Death. 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 ...
A pattern, for a given cellular automaton, consists of a finite set of cells together with a state for each of those cells. [6] A configuration contains a pattern when the states of the cells in the pattern are the same as the states of the same cells in the configuration (without translating the cells before matching them).
As in Conway's Game of Life, at any point in time each cell may be in one of two states: alive or dead. The Critters rule is a block cellular automaton using the Margolus neighborhood. This means that, at each step, the cells of the automaton are partitioned into 2 × 2 blocks and each block is updated independently of the other blocks.
The Rule 110 cellular automaton (often called simply Rule 110) [a] is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. [2]
The fumarole, a period-5 oscillator in Conway's Game of Life.The two live cells appearing at the top of the pattern every five generations are considered a spark. In Conway's Game of Life and similar cellular automaton rules, a spark is a small collection of live cells that appears at the edge of some larger pattern such as a spaceship or oscillator, then quickly dies off.
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