Doyle Spirals

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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 and are positive real numbers. Then six circles of successive radii close up exactly when placed tangent to one another around a circle of radius 1.


You can vary the values of the parameters and , 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.


Contributed by: Jaime Rangel-Mondragon (July 2014)
Open content licensed under CC BY-NC-SA




[1] J. Leys. "Hexagonal Circle Packings and Doyle Spirals." (Feb 2005)

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