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
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Details
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.
Reference
[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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