Dimension estimate for a set obtained from a three-dimensional non-periodic self-affine tiling (Q2762675)
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scientific article; zbMATH DE number 1688870
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dimension estimate for a set obtained from a three-dimensional non-periodic self-affine tiling |
scientific article; zbMATH DE number 1688870 |
Statements
2 March 2003
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Pisot number
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self-affine tiling
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Hausdorff dimension
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Dimension estimate for a set obtained from a three-dimensional non-periodic self-affine tiling (English)
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For a three-dimensional self-affine tiling generated by the Pisot number satisfying \(x^4=x^3+x^2+x+1\), the Mauldin-Williams graph is used to give explicit bounds for the Hausdorff dimension of an associated subset of the complex plane. Numerical evidence suggests the upper bound obtained is the exact value.
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