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The Art and Mathematics of Genji-Ko

You might think there’s unlikely to be any interesting mathematics arising from incense appreciation, but that’s only because you’re unfamiliar with the peculiar character of Muromachi (室町) era (circa 1300-1500) Japanese nobles. There has never been a group of people in any time or place who were so keen to display their sophistication and refinement. It wouldn’t do to merely put out a few sticks of incense - no, you would have to prove that your taste was more exquisite, your judgement more refined, your etiquette more oblique.

Every educated person of the Muromachi era would be intimately familiar with The Tale of Genji and would know the themes, season, and characters associated with each chapter by heart, giving each pattern a literary resonance. However, its cultural influence extends beyond the few who actually play the game - the patterns show up fairly often as a motif in contemporary Japanese graphic design, and it’s especially popular on traditional goods such as kimono: I spent some time trying to find some elegant heuristic that would nudge the layout algorithm to produce those four without breaking any of the others, but the rules were more complex than simply listing the special cases (and none of them correctly handled Yūgiri (夕霧) which I’ll discuss below.)

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