Four-Color Outer Median Cellular Automata on Graphs
Four-Color Outer Median Cellular Automata on Graphs
Outer median (OM) rules on cellular automata (CA) calculate the color of the next step of the active cell by looking at the neighbors of the active cell and taking the floor of the median of the colors of those neighbors. Then basic rules are applied on the resultant pairs: {active cell, floor of median of neighbors}. This effectively allows CA rules to be taken "off the lattice", whereby an active cell can have any number of neighbors and still have the same number of rules. Therefore, the CA translates naturally to application on a network of nodes (graph), each node representing an active cell, and the node neighbors representing the neighbors of the active cell. The node evolution is shown as an array plot, for 50 steps.