127-crossing Self-similar Knot

The starting point for this knot is a three-crossing knot that has been carefully arranged to allow seamless iteration. The strands, smoothly varying for the most part, also contain sharp corners, a design esthetic borrowed from Celtic knots. Two of the three crossings in the starting knot are replaced with a scaled-down copy of the group of three crossings, incorporated in such a way that the iterated knot is still unicursal. The scaling factor is the inverse of the square root of 3, and there is a 90 degree rotation with each iteration. Five iterations are performed in similar fashion, resulting in a complex knot possessing self similarity. "127-crossing Self-similar Knot" is a limited edition of 50 digital prints created in 2009. The image size is 12" x 10".

Copyright 2009 Robert Fathauer