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Additive Cellular Automata

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number of colors
2
3
4
5
6
monoid
dependency range
1
2
3
4
5
6
initial cell color
initial background color
number of steps
50
separation
0
For every
k
-element commutative monoid and every range size
s
, there is an additive
k
-color cellular automaton in which the color of a cell is simply the sum (in the monoid operation) of the colors of
s
cells on the previous step. These automata always exhibit global nested structure when begun from a single cell.
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