Self Similar Knot No. 2

The starting knot for this artwork, which is based on the 3-crossing trefoil knot, has 9 crossings. It was designed with sufficient geometric regularity to allow iterative replacement of a portion of the knot with a scaled down copy of the knot. Six such iterations were carried out to obtain the knot shown here. Two other views of the knot, which show its trefoil character more clearly, are shown at the bottom of this page. The final knot has the form of three orthogonal spirals that descend as the curvature decreases. The knot was constructed using the program KnotPlot and then exported to PhotoShop for touching up. "Self Similar Knot No. 2" is a limited edition of 50 digital prints created in 2009. This print was featured on the cover of the March, 2012 issue of The College Journal of Mathematics.

Digital art print of a three-dimension knot created by iterating a trefoil knot.

Two other views of the knot:

Copyright 2009 Robert Fathauer