Keep Going (Spheres VIII)

Apollo small3

This, like most of my images from the Sphere series, has its origin in a 2-dimensional picture. Below you see (parts of) the Apollonian Gasket. Descartes and Princess Elisabeth of the Palatinate discussed formulas for a fourth circle tangent to four other circles, more than 300 years circle packings became fashionable.

Descartes3a

Now, in three dimensions, begin by placing four equally sized spheres into a larger sphere, like so:

Master 00

Start filling the empty space with more spheres, each as large as possible to touch four other spheres.

Master 0

Keep going.

Master 1

and going, and going.

Master 9

Finally, when you are tired and done, remove the first four largest spheres to create an empty space, and have a peek inside. What you see might look like the image at the top.

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