This tessellation is based on the Gosper 13 space-filling curve, discovered by Fukuda et al., with deformed rhombus tiles filled with a bird. The generated segments of the curve indicate whether a rhombus must be rendered to its left (blue bird) or to its right (yellow bird). Each rhombus consists of two equilateral triangles. One triangle has its base on a curve segment, and one of its two remaining edges is the base for the other triangle. However, it is not obvious (for me) which of the two edges. I used some heuristical rules, as well as a search algorithm to determine the correct edges. After three iterations the tessellation has 13 * 13 * 13 = 2197 tiles. The curve starts at the top center, and ends at the right center. You can follow the curve on the dark edges of the birds.
As far as I know, this is the first tessellation of a space-filling curve that is tiled with a rhombus shape.
The image is 12000 x 12000 pixels, and can therefore be printed large.
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…