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Square Spiral Tiling

​
rotation
5.12
p, q
3, 1
orbit mode
fixed
spiral
Space-filling squares arranged in spirals can orbit either around the spiral origin or around the fixed centers.

Details

This Demonstration is based on a method published by Danny Calegari[1]. The spirals depend on a pair of complex numbers,
a
and
b
. The set of precalculated values is determined by solving the equations
a+
1
a
+b+
1
b
=4
,
p
a
q
b
=1
,
for
a
and
b
, where
p
and
q
are arbitrary integers. From the multiple solutions, suitable ones have to be selected.

References

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

External Links

Permanent Citation

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