Three-dimensional cellular automaton: Difference between revisions
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Revision as of 17:50, 29 September 2022
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A three-dimensional cellular automaton operates in three-dimensional space. Like one- and two-dimensional cellular automata, 3D automata may operate in different neighbourhoods, be totalistic or non-totalistic, isotropic or non-isotropic.
Most commonly, the 3D space is thought of as being divided into a grid of cubic cells. For a 3D version of the Moore neighbourhood, each cell is at the center of a 3 × 3 × 3 neighbourhood, giving it 26 neighbouring cells it touches. For a 3D version of the von Neumann neighbourhood, a cell has 6 neighbours with which it shares a face.
3D Game of Life
In 1987, Carter Bays wrote a paper analyzing what it meant to project the Game of Life into a 3D universe with cubic cells in which a cell has 26 neighbours instead of the 8 neighbours in 2D. Bays proposed two criteria for such a rule having Life-analogous behaviour:
Simply applying the B3/S23 rule in 3D space does not meet criterion 2. Having birth on 4 neighbours or fewer results in lightspeed expansion similar to B2 rules in 2D.
In general, the increase from 8 2D neighbours to 26 3D neighbours means there are vastly more possible rules. Bays developed several theorems to reduce the number of candidate rules. He found that rule B6/S57 produces behaviour similar to Life.[1]
See also
References
- ↑ Carter Bays (1987). "Candidates for the Game of Life in Three Dimensions". Department of Computer Science, University of South Carolina.