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.
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A self-similar dendrite with finite self-similar boundary has an associated sprout graph that determines its combinatorial properties and topological structure.
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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.
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Self-similar dendrites with finite boundary and P-sprouts
A self-similar dendrite with finite self-similar boundary has an associated sprout graph that determines its combinatorial properties and topological structure.