On the dimension of deterministic and random Cantor-like sets (Q1902185)
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scientific article; zbMATH DE number 817716
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the dimension of deterministic and random Cantor-like sets |
scientific article; zbMATH DE number 817716 |
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On the dimension of deterministic and random Cantor-like sets (English)
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31 March 1996
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The authors extend Moran's construction of fractals to an asymptotic, respectively random type construction. In the first case the contraction ratios converge in a certain Cesàro-like mean to zero. The random construction is determined by an ergodic stationary process. They unify results concerning box and Hausdorff dimension known for deterministic and random Cantor-like sets. The constructions involve only weak restrictions on the geometry.
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box dimension
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fractals
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Moran's construction
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ergodic stationary process
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Hausdorff dimension
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random Cantor-like sets
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