Square Spiral Tiling

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Space-filling squares arranged in spirals can orbit either around the spiral origin or around the fixed centers.

Contributed by: Dieter Steemann (August 2017)
Open content licensed under CC BY-NC-SA



This Demonstration is based on a method published by Danny Calegari [1]. The spirals depend on a pair of complex numbers, and . The set of precalculated values is determined by solving the equations



for and , where and are arbitrary integers. From the multiple solutions, suitable ones have to be selected.


[1] D. Calegari. "Kenyon's Squarespirals," Geometry and the Imagination (blog). (Jan 13, 2013) lamington.wordpress.com/2013/01/13/kenyons-squarespirals.

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