Taxicab Voronoi Diagram by a Cellular Automaton

The Voronoi diagram for a finite set of points S in the plane is a partition of the plane into polygons, each of which consists of all the points in the plane closer to one particular point of S than to any other. Usually, the Euclidean distance is used, but this Demonstration uses the taxicab distance to make a Voronoi diagram. It happens that three-color cellular automaton 6745720851345 can be used for taxicab Voronoi diagrams.