Self-similar Knot No. 1

A starting knot was created that possessed sufficient geometric regularity to allow iterative replacement of a portion of the knot with a scaled down copy of the knot. Three such iterations were carried out to obtain the knot shown here. The starting knot and first two iterations are shown at the bottom of this page. In addition, the path of the strands was smoothed out so that strand in the final knot curves gracefully, as opposed to being a series of straight line segments that change angle abruptly. The knot was constructed using the program KnotPlot and then exported to PhotoShop for touching up. "Self-simiar Knot No. 1" is a limited edition of 50 digital prints created in 2009. The image size is 10" x 13".

The starting knot and first two iterations:

Copyright 2009 Robert Fathauer