"Squaring of a torus" by Timothy Budd: any graph properly embedded in the torus yields a two-parameter family of periodic square tilings of the plane. Interactive app: http://hef.ru.nl/~tbudd/squaring/index.html … See also this blog post by Danny Calegari: https://lamington.wordpress.com/2013/01/13/kenyons-squarespirals/ …pic.twitter.com/z9YURKlbox
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Here's a GIF of a "squarespiral" from Calegari's blog post. P.S. Since tilings by squares map onto electrical circuits (Brooks, Smith, Stone, Tutte 1941 http://www.squaring.net/history_theory/brooks_smith_stone_tutte.html …) the two parameters can be interpreted as net currents around the two cycles of the torus!pic.twitter.com/BvS3OXfjig
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