Estimate for 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 [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 two and three dimensions to within 0.05% and 0.6%, respectively, and we provide predictions for dimensions 4-8.
Farr
R S
RS
Unilever R&D, Olivier van Noortlaan 120, AT3133 Vlaardingen, The Netherlands. robert.farr@unilever.com
Griffiths
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