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From 2014.igem.org

Form a growing snowflake with Cellular Automaton

A growing snowflake can be programmed with two-dimensional cellular automaton[]. The cellular space is defined as a two - dimensional square lattice of cells with size of n*n. Every cell has two states, on and off, represented by “1” or “0” respectively, and has four orthogonally adjacent cells as neighborhood. Its evolution rule directs how cells change states from one discrete time point to the next and it is that: if a cell is off, it can change state to be on at the next time point only when one out of its four neighborhood is on; if a cell is on, it will remain on forever.
For a cell with coordination of , at time point , its state can be shown as. Then the evolution rule is:

Let initial state as all cells off except for the center four “on” cells. As time increases, a growing snowflake forms with less than 10 steps (one step equals to one time point). Figure 1 shows how a snowflake grows up at time point 6. Figure 2 shows a dynamic pattern of it.

Figure 1

Figure 2