# Four-Color Outer Median Cellular Automata on the Grid

Four-Color Outer Median Cellular Automata on the Grid

Outer median cellular automata (CA) are a functional form of the CellularAutomaton function in Mathematica. The color of the active cell on the next step is determined by first taking the median of the neighbors of the active cell up to a certain radius and then taking the floor of the median. In two dimensions, radius 1 means the eight neighbors around the central active cell, and radius 2 means out to the sixteen neighbors around the eight neighbors around the central active cell. The pairs {active cell color, floor of median of neighbors} are then mapped to rules in color spaces as usual. Here there are four colors.