A New Method for Designing Iterated Knots

Robert Fathauer
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 251–258 Regular Papers


A new method for designing iterated knots is described. The method utilizes a starting curve in which smaller copies of the curve are embedded. Points along the curves are connected by strands to form a knot, which is iterated by replacing the contents of the smaller curves with the contents of the larger curve. The method possesses considerable design flexibility, allowing the creation of stylized and esthetically pleasing iterated knots.