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).

中文翻译：

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分形线染色的设计：以文化与分形数学为中介的算法设计案例

数以百万计的人拥有并穿着千鸟格式的服装。该模式具有一个有趣的基本图形和一组典型的对称性。图案的起源在于特定的编织类型。在本文中，我将应用计算技术对这种古老的装饰图案进行现代化。特别是，我描述了一种利用分形结构富集池状结构的方法。尽管在Bridges 2015中显示了第一条分形线池状结构，但仍然存在一些基本问题。本文解决了以下问题：当分形结构越来越精细时，原始的浆状结构是否会作为一种限制情况出现？我们可以从一个公式描述所有模式的意义上证明模式是规则的吗？在制作这些分形时，pied-de-poule有什么特别之处？本文的结果和技术可以预见时尚的未来，其中装饰性图案（包括花絮）将成为我们全球文化的一部分，就像现在一样，但是将使用新技术以更精致的方式进行渲染这些新技术包括数字制造技术，例如激光切割和3D打印，还包括计算和数学工具，例如Lindenmayer规则（最初旨在描述植物的算法美感）。