The Mystery Curve-Part 2: Local Symmetry and Frieze Groups [Lecture Notes

Abstract

In this article, we continue to study the mystery curve, which was originally named by Farris [1] and discussed in the first part of this two-part article in IEEE Signal Processing Magazine [2]. The mystery curve has an N -fold property with additional local symmetry as shown in Figure 1. In particular, we focus on symmetric patterns, including translation, reflection, rotation, and glide reflection. This class of patterns is called a frieze group . We show how to construct frieze groups with trigonometric functions and extend this method to the mystery-curve design.