Extensions to the Model Excited States

In an interesting variant of the CA model, cells can adopt excited states. This has been used to model the spatial waves observed in the Zaikin-Zhabotinsky reaction. 

In this model, run on a square grid, each unit can adopt one of N states, 0, 1, 2, 3. (N - 1) states other than 0 are excited states. The neighbors are those cells that share an edge with the target cell (a von Neumann neighborhood). The transition rules can be divided into two types first we have reaction rules  

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These rules mimic the spontaneous first order reaction of a chemical (a cell in state x) that transforms into a different chemical (the cell in state x + 1). 

Diffusion rules relate the future state of the target cell to those of neighboring cells. This mimics a second order reaction  

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