This fractal Square Limit consists of white and black swans. There are two main differences with M.C. Escher's famous Square Limit. The basic figure of the entire square contains triangles that are deformed into swans in such a way that all swans have the same shape; they are only rotated and/or scaled, but not mirrored as in Escher’s woodcut. Furthermore, a swan generates towards the border two smaller swans, with half the area. This creates a fractal structure, with (in theory) an infinite number of microscopic swans at the border. The substitution scheme at the diagonals has been changed in a consistent manner, so that one swan there also generates two smaller swans. As a result, the shape of the overall image becomes a non-regular octagon instead of a square. (The longer sides of the octagon are the square root of 2 longer than the shorter sides.) The swans in the middle, and therefore their offspring, are rotated 45 degrees compared to Escher's original.
My training as a mathematician and my experience as a software programmer are the basic elements for designing my works of art. Since my retirement in 2019 I have started creating digital art with a mathematical slant. The works of M.C. Escher are a source of inspiration. Thanks to programs.. Read more…