We apply the basic transformation to a square 3 and 4 times, then take its dual.
This is the pattern you generate starting with a 4x4 array of squares, then apply 2 iterations of the next algorithm, relax then make the dual.
This is the pattern you get if you start with an octagon with radial lines (wheel), apply the basic iteration once, then take the dual. The next two images are the result of applying the "next" transformation to the octagonal shape above. And the final image is the dual of the third.
Two images from the pentagon series, the first is the result of three iterations, starting with the pentagon with radial spokes. The second is the dual of the first.
These next two images are partially relaxed versions of previous pentagonal patterns. I say partially because I applied the relaxation stage between the second and third applications of the edge replacement algorithm.
Finally, for the really ambitious, this example shows what happens when you apply the standard transformation to the previous dual pattern. This is a 2400x2400 image.
(c) John Whitehouse 2010 - 2023