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Doyle Spirals

a
rotate
b
zoom
Doyle spirals are stunning patterns made of tangent circles, each of which touches six others. The method of generating these and many other patterns started with Peter Doyle's now-historical observation: suppose
a
and
b
are positive real numbers. Then six circles of successive radii
a,b,b/a,1/a,1/b,a/b
close up exactly when placed tangent to one another around a circle of radius 1.
You can vary the values of the parameters
a
and
b
, which for some choices make the pattern overlap. You can rotate, zoom, and drag the light blue circle to center the pattern. The rotation is performed around this circle.
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