Four knot

A Thue-Morse tiling (broken link) weave, colored by connectivity. The tiles are square, with two orientations of the motif, and the edges of tiles run diagonally relative to this image.

The motif consists of four chiral spline segments, suggested by a sketch Ted Bell showed me.

Why this works (nested circuits in this weave pattern) is a mystery to me. How would a larger Thue-Morse pattern with the same motifs be connected? I designed the motif, shading and coloring, but I didn't design the pattern; I found it.

"There is no scientific discoverer, no poet, no painter, no musician, who will not tell you that he found ready made his discovery or poem or picture - that it came to him from outside, and that he did not consciously create it from within." William Clifford (From a lecture to the Royal Institution titled "Some of the conditions of mental development")

Download for 1400 x 1400 px. version.

Space Software (broken link), Matlab, and Paint Shop Pro


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There are no restrictions on use of this image. Claiming to be the originator or owner, explicitly or implicitly, is bad karma. A link (if appropriate), a note to markdow30@gmail.com, and credit are appreciated but not required.