# Estimate for the fractal dimension of the Apollonian gasket in d dimensions

R. Farr, E. Griffiths

*Physical Review E* 81, 61403 (2010)

#fractals#spherepacking#fractalstructures

We derive an estimate of the fractal dimension of the Apollonian gasket in d dimensions.

We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions in order to predict the Hausdorff dimension of the Apollonian gasket in dimensions 2 and above. Our approximate results agree with published values in 2 and 3 dimensions to within 0.05% and 0.6% respectively, and we provide predictions for dimensions 4 to 8.

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