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Peter Doyle discovered the fact that a set of 6 circles arranged around a central circle ( a
‘flower’) may be extended to an infinite
hexagonal circle packing of the plane. ( which is possibly overlapping ,i.e. not coherent). With this knowledge, it is possible to construct an infinite amount of circle arrangements,
as proven by Stephenson et.al

The circle packing patterns that are generated this way can be transformed onto the
surface of a sphere by projection on the Riemann sphere, or through the use of a sphere
inversion. Replacing all the circles by spheres of the same diameter produces images that
are graphically more appealing. Both of these transform circles to circles and spheres to
spheres.

 

 

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