Elementary fractal geometry. 5. Weak separation is strong separation

Christoph Bandt, Michael F. Barnsley
4/7/2024
math.DScs.CL

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Abstract

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.

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Cite this paper

@article{bandt2024elementary,
  title  = {Elementary fractal geometry. 5. Weak separation is strong separation},
  author = {Christoph Bandt and Michael F. Barnsley},
  year   = {2024},
  eprint = {2404.04892},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2404.04892v1}
}

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