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A special class of cellular automata are totalistic cellular automata. The state of each cell in a totalistic cellular automaton is represented by a number (usually an integer value drawn from a finite set), and the value of a cell at time t depends only on the sum of the values of the cells in its neighborhood (possibly including the cell ...
A cellular automaton (CA) is Life-like (in the sense of being similar to Conway's Game of Life) if it meets the following criteria: 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")
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 ...
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 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 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 ...
If the left, center, and right cells are denoted (p,q,r) then the corresponding formula for the next state of the center cell can be expressed as p xor (q or r). It is called Rule 30 because in binary, 00011110 2 = 30. The following diagram shows the pattern created, with cells colored based on the previous state of their neighborhood.
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 ...
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