A point is moving on a square lattice with periodic boundary conditions. Initially the lattice is covered with color 0. When the ant leaves a site, it increases the color by one modulo 4: 0->1->2->3->0->1->2... . The ant can only go right or left, according to the color of the site it moves to. The highway builder uses RLRL for 0123, while the castle builder uses RLLR for 0123.