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March 30th 2014

Recursive Appolonian gaskets

Francesco de Comité has a very interesting set featuring recursive Apolonian gaskets. As far as I can guess, these pictures are created as follows.

Apolonian gaskets are fractal coverings of a disk by disks of smaller sizes. The images of fdecomite are created by filling the disks of an Apolonian gasket by Apolonian gaskets, and iterating the procedure. As there are different types of gaskets, one can combine them in many ways (including possible rotations at each iteration) and obtain a great variety of dense fractal patterns. For instance, a few Sierpinski triangles lurk in the images below.

[Update:] A short paper describing the algorithm is available here.

fdecomite, Verifying4 (2013), digital image.

fdecomite, Snowflakes (2012), digital image.

fdecomite, Filling by circles (2012), digital image.