On Hausdorff dimension of recurrent net fractals

Stella, Sergio

doi:10.1090/S0002-9939-1992-1094507-X

On Hausdorff dimension of recurrent net fractals
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Proc. Amer. Math. Soc. 116 (1992), 389-400 Request permission

Corrigendum: Proc. Amer. Math. Soc. 121 (1994), 1309-1311.

Abstract:

We estimate the Hausdorff dimension of recurrent net fractals showing that it coincides with the box-counting dimension. This is done for geometric constructions in a complete metric space, generalizing well-known theorems about self-similar sets. In particular, it follows that what is really essential in the dimension estimates of self-similar sets are their metric features and not the dynamical ones.

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