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

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

Physical Review E 81, 61403 (2010)

R. Farr, E. Griffiths

LQ placeholderWe 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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Network valuation in financial systems

P. Barucca, M. Bardoscia, F. Caccioli, M. D’Errico, G. Visentin, G. Caldarelli, S. Battiston

Mathematical Finance

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A. Mozeika, B. Li, D. Saad

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T. Coolen, M. Sheikh, A. Mozeika, F. Aguirre-Lopez, F. Antenucci

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M. Reeves, S. Levin, T. Fink, A. Levina

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A. Mozeika, T. Coolen

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F. Vanni, P. Barucca

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