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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")
There are continuous automata. These are like totalistic cellular automata, but instead of the rule and states being discrete (e.g. a table, using states {0,1,2}), continuous functions are used, and the states become continuous (usually values in ). The state of a location is a finite number of real numbers.
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.
Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. [2] This implies that, in principle, any calculation or computer program can be simulated using this automaton. An example run of the rule 110 cellular automaton over 256 iterations, starting from a single cell.
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 ...
The cells outside the image are all dead (white). An orphan in Life found by Achim Flammenkamp. Black squares are required live cells; blue x's are required dead cells. In a cellular automaton, a Garden of Eden is a configuration that has no predecessor.
Even though all live cells are constantly dying, the small birth requirement of two cells means that nearly every pattern in Seeds explodes into a chaotic mess that grows to cover the entire universe. Thus, in Wolfram's classification of cellular automata, it is a Class III automaton, in which nearly all patterns evolve chaotically. [1]
Langton's loops are a particular "species" of artificial life in a cellular automaton created in 1984 by Christopher Langton. They consist of a loop of cells containing genetic information, which flows continuously around the loop and out along an "arm" (or pseudopod), which will become the daughter loop. The "genes" instruct it to make three ...