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arXiv · 1006.1606

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

R. S. Farr·E. Griffiths
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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. {\bf 131} 244104 (2009)] in order to predict the Hausdorff dimension $d_{A}$ 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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R. S. Farr, E. Griffiths. 2010-06-08. Estimate for the fractal dimension of the Apollonian gasket in d dimensions. https://doi.org/10.1103/physreve.81.061403

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