![]() The word "totalistic" stems from the fact that evolution in a totalistic CA depends only on the total number of live cells in a given cell's neighborhood similarly, in outer-totalistic CAs, evolution depends on the total number of outer cells, rather than their specific alignment. For example, Fredkin (sometimes referred to as "Replicator 2") has the totalistic rulestring 13579 the equivalent rulestring in B/S notation is B1357/S02468. Totalistic CAs are described by totalistic rulestrings: strings of digits specifying the live cell counts which will cause a given cell to be alive in the next generation. For example, the following two configurations may evolve differently in an outer-totalistic CA, but must be treated the same by a totalistic CA: The two definitions differ in that in the second case, the transition function may afford special consideration to the state of the cell itself. The rest of this article uses the more narrow definition. In common parlance, "totalistic" is also often (but incorrectly) used as a synonym for "outer-totalistic" / "semi-totalistic", meaning that the new state of a cell is a function of both the total number of live cells surrounding the cell, and the state of the cell itself. In the program Mirek's Cellebration, totalistic cellular automata fall into a family called Vote for Life, which is named after the rule Vote (B5678/S45678). Conway's Game of Life (B3/S23), on the other hand, is not totalistic: a live cell with three neighbors will survive to the next generation, but a dead cell with four neighbors will not get born. For example, the rule given by the rulestring B3/S2 is totalistic any cell will be alive in the next generation if it has exactly three live cells (including the cell itself) in its neighborhood, and dead otherwise. įor a given Life-like rule to be totalistic, the following condition is necessary and sufficient: for all 1 ≤ n ≤ 8, a live cell survives with n - 1 neighbors iff a dead cell gets born with n neighbors. There are precisely 2 10 = 1024 different totalistic CAs, compared to 2 18 = 262,144 outer-totalistic CAs. In a more narrow sense, a Life-like cellular automaton is said to be totalistic / inner-totalistic when the new state of a (live or dead) cell in the next generation can be expressed as a function of the total number of live cells in its neighborhood, counting the cell itself. Totalistic Life-like cellular automaton can refer to two related but distinct classes of cellular automata.
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