Abstract / Synopsis
Millions of people own and wear pied-de-poule (houndstooth) garments. The pattern has an intriguing basic figure and a typical set of symmetries. The origin of the pattern lies in a specific type of weaving. In this article I apply computational techniques to modernize this ancient decorative pattern. In particular I describe a way to enrich pied-de-poule with a fractal structure.
Although a first fractal line pied-de-poule was shown at Bridges 2015, a number of fundamental questions still remained. The following questions are addressed in this article: Does the original pied-de-poule appear as a limit case when the fractal structure is increasingly refined? Can we prove that the pattern is regular in the sense that one formula describes all patterns? What is special about pied-de-poule when it comes to making these fractals? Can the technique be generalized?
The results and techniques in this article anticipate a fashion future in which decorative patterns, including pied-de-poule, will be part of our global culture, as they are now, but rendered in more refined ways and using new technologies. These new technologies include digital manufacturing technologies such as laser-cutting and 3D printing, but also computational and mathematical tools such as Lindenmayer rules (originally devised to describe the algorithmic beauty of plants).
Loe M. Feijs, "Designing Fractal Line Pied-de-poules: A Case Study in Algorithmic Design Mediating between Culture and Fractal Mathematics," Journal of Humanistic Mathematics, Volume 10 Issue 1 (January 2020), pages 240-266. DOI: 10.5642/jhummath.202001.11. Available at: https://scholarship.claremont.edu/jhm/vol10/iss1/11