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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.04892 |
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| _version_ | 1866909163101093888 |
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| author | Bandt, Christoph Barnsley, Michael F. |
| author_facet | Bandt, Christoph Barnsley, Michael F. |
| contents | For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We show that any finite type self-similar set can be represented as a graph-directed construction obeying the open set condition. The proof is based on a combinatorial algorithm which performed well in computer experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elementary fractal geometry. 5. Weak separation is strong separation Bandt, Christoph Barnsley, Michael F. Dynamical Systems Computation and Language 28A80, 11A63, 37B10, 54B15, 68Q45 For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We show that any finite type self-similar set can be represented as a graph-directed construction obeying the open set condition. The proof is based on a combinatorial algorithm which performed well in computer experiments. |
| title | Elementary fractal geometry. 5. Weak separation is strong separation |
| topic | Dynamical Systems Computation and Language 28A80, 11A63, 37B10, 54B15, 68Q45 |
| url | https://arxiv.org/abs/2404.04892 |