Apollonian Circle Packings

The curvature of 4 mutually tangent circles is determined by Descartes' Theorem. There are lots of nice pictures of this on the Apollonian gasket Wikipedia page.

The (0,0,1,1) circle packing

I made some pictures of this special case and added them.

gif

This animation transitions between circles with finite radius and the limiting case with infinite radius above.

tags: mathart | animation | sage

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