Definition
A block cellular automaton consists of the following components:
- A regular lattice of cells
- A finite set of the states that each cell may be in
- A partition of the cells into a uniform tessellation in which each tile of the partition has the same size and shape
- A rule for shifting the partition after each time step
- A transition rule, a function that takes as input an assignment of states for the cells in a single tile and produces as output another assignment of states for the same cells.
In each time step, the transition rule is applied simultaneously and synchronously to all of the tiles in the partition. Then, the partition is shifted and the same operation is repeated in the next time step, and so forth. In this way, as with any cellular automaton, the pattern of cell states changes over time to perform some nontrivial computation or simulation.
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