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 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. © 2010 The American Physical Society.