Here's another pattern that comes from a grid of octagons. It would be orange octagons and white square but the focus is on the loops of four octagons. Inserted between every pair of octagons is a triangle(red) and a square(blue). The pattern of insertion is alternating. For instance, if you follow a loop of polygons (clockwise) that surrounds a hole that resembles an S, then you will see a triangle-square that bends to the right where as the next triangle-square bends to the left. In fact, the original white squares (from a octagon&square tiling with vertex 488) are transformed into the distorted S's and Z's seen in the pattern.