Emergence of Turing Patterns in a Simple Cellular Automata-Like Model via Exchange of Integer Values between Adjacent Cells

Figure 4

Schematic of token exchange. Each cell can contain multiple tokens concurrently. These are labeled with an integer value . Some tokens are moved to adjacent cells. The residual token ratio r is the fraction of unchanged (unmoved) tokens in each cell, where is the number of blocks in cell at time . (1) A proportion, of the tokens evenly diffuse toward the six neighboring cells and have their labels incremented by 1 upon arrival. (2) A proportion, of the tokens remain in the original cell and have their labels incremented by 1. (3) The residual, tokens remain in the original cell without modification of their integer labels. If the number of tokens is not an integer multiple of 7, the remainder of the tokens are distributed between the adjacent cells with equal probability.