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The cyclic cellular automaton by David Griffeath This
is a self-replicating cellular automaton. It is made of a regular
grid of "cells", each containing a "state" chosen from a finished
set (4 in this case: yellow, light orange, dark orange, red): The CA evolves over time: The state of a cell at time t+1 depends on its state at time t and the state of its neighbours. At each time step, a rule (called Transition Function) is applied simultaneously to all cells in the grid, producing a new "generation" of cells entirely dependent on the previous generation. Each cell remains unchanged until some neighboring cell has a modular value exactly one unit larger than that of the cell itself. In other words, the transition function is: a cell changes from one state (i) to the next (i+1) in the state cycle as soon as i+1 is present in at least 3 neighboring cells :  From a random initial state of the grid, we obtain this type of complex results:
Grid at step 2500:
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