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.

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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.

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


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Details

Reference

[1] J. Leys. "Hexagonal Circle Packings and Doyle Spirals." (Feb 2005) www.josleys.com/articles/HexCirclePackings.pdf.



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