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

Figure 6

Flow chart of the calculations. (a) Two-state cells are assumed, namely, black and white cells . (b) Each cell can contain multiple tokens simultaneously. These are labeled with integer values. (c) The black cells are the source of the tokens. This is where the first parameter is set: the token production number is the initial number of tokens on a black cell at each time-step. (d) Some tokens are moved to adjacent cells. The residual token ratio is the fraction of unchanged (unmoved) tokens in each cell. The token distribution processes shown in Figure 4, are applied to each cell. In each cell, transit tokens have their integer labels changed from to . Under this process, some tokens remain in their original cell without modification. Incremental labeling is repeated until the maximum label number reaches (where is an fixed even integer). (e) Using the token dissipation rate , the number of tokens in a cell is set to zero if there are fewer than tokens. (f) Processes (c), (d), and (e) are applied to all cells in the hexagonal grid and the state of cells at the next time-step is determined. (g) After the movement and modification of the tokens, each subsequent cell state is determined by the ratio of the number of tokens labeled or smaller in the cell to the total number of tokens in the cell, according formula (3).