Visually pleasing knot projections

Abstract

In this short article, I discuss the æsthetics of knot projections and introduce software that creates two-dimensional knot diagrams optimized for visual appearance. The software is in the form of a documented and self-contained suite of functionality written in the R programming language (that is, a ‘package’): knotR. The package leverages the graphical capabilities of the popular vectorized graphics software inkscape. Different aspects of knot appearance are discussed, and a framework for objectively optimizing the visual appeal of a knot projection is given. I use the software to create a wide range of knot diagrams.

GRAPHICAL ABSTRACT

Keywords:

• Knot theory
• knot projections
• crossing number
• visual appearance
• aesthetics
• symmetry

2010Mathematics Subject Classifications:

• Primary 57K10-XX
• 32-XX

Acknowledgments

The author would like to thank an anonymous referee whose insightful comments led to a much-improved manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).