Twice Iterated Knot No. 1
The starting point for this knot is a nine-crossing knot that has been carefully arranged to allow seamless iteration. Four regions of this starting knot are replaced with a scaled-down copy of the full starting knot, incorporated in such a way that the iterated knot is still unicursal. These same four regions are then replaced with a scaled-down copy of the iterated knot, resulting in a complex knot possessing self similarity. The smaller images below show the starting knot and the knot after one iteration. The print shows the knot after two iterations.
"Twice Iterated Knot No. 1" is a limited edition of 50 digital prints created in 2008. The image size is 9" x 15". This print won Third Prize in the 2009 Exhibition of Mathematical Art at the Joint Mathematics Meetings in Washington, DC.
The starting knot and the knot after one iteration:
Copyright 2008 Robert Fathauer