Estimate for the fractal dimension of the Apollonian gasket in d dimensions
Abstract
We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions [R. S. Farr and R. D. Groot, J. Chem. Phys. 131 244104 (2009)] in order to predict the Hausdorff dimension dA 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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