Abstract
The Apollonian packing of circles has long been the prototype of a self-inverse set.1 More recently, physicists have speculated on its role in the long-time behavior of soap cells and froths.2 It is suprising, therefore, that its scaling properties are still poorly understood. Mandelbrot3 has termed the fractal complement of this space-filling packing the “Apollonian gasket.” Here we present some new results on the fractality of Apollonian gaskets. In particular, we show they are multifractals.
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