Automata are axiomatically defined to generate topologically self-similar spaces, with algorithms for k-tuples of equivalent addresses and finite approximations, plus discussion of realization as self-similar sets.
Lipschitz equivalence of fractals and finite state automaton
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abstract
The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using finite state automata, we construct a bi-Lipschitz map between two fractal squares which are not totally disconnected. This is the first non-trivial map of this type. We also show that this map is measure-preserving.
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math.MG 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
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Elementary fractal geometry. 4. Automata-generated topological spaces
Automata are axiomatically defined to generate topologically self-similar spaces, with algorithms for k-tuples of equivalent addresses and finite approximations, plus discussion of realization as self-similar sets.