Elementary fractal geometry. 5. Weak separation is strong separation
Year: 2025
Type: article
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.
Source: Nonlinearity
Authors: Christoph Bandt, Michael F Barnsley
Institutions: Universität Greifswald, Australian National University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4410501696