Designing fractal line pied-de-poules:a case study in algorithmic design mediating between culture and fractal mathematics

Millions of people own and wear pied-de-poule (houndstooth) garments. Thepattern has an intriguing basic figure and a typical set of symmetries. The originof the pattern lies in a specific type of weaving. In this article, I apply compu-tational techniques to modernize this ancient decorative pattern. In particular Idescribe 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 numberof fundamental questions still remained. The following questions are addressedin this article: Does the original pied-de-poule appear as a limiting case whenthe fractal structure is increasingly refined? Can we prove that the pattern isregular in the sense that one formula describes all patterns? What is specialabout pied-de-poule when it comes to making these fractals? Can the techniquebe generalised?The results and techniques in this article anticipate the future of fashion wheredecorative patterns, including pied-de-poule, will be part of our global culture,as they are now, but rendered in more refined ways, using new technologies.These new technologies include digital manufacturing technologies such as laser-cutting and 3D printing, but also computational and mathematical tools suchas Lindenmayer rules (originally devised to describe the algorithmic beauty ofplants).