Abstract

We introduce a class of random sets in ℝ2 that include McMullen's “generalized Sierpinski carpets”. We give exact expressions for the Hausdorff and Bouligand-Minkowski (box) dimensions of these sets, and find in particular that typically they are not equal. Our expression for the Hausdorff dimension isnot what one would expect by analogy with McMullen's formula for the Hausdorff dimension of a generalized Sierpinski carpet.

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