Isomorphism of Hierarchical Structures
Charles Radin, Lorenzo Sadun

TL;DR
This paper explores how different definitions of isomorphism affect the classification and matching rules of hierarchical structures like Fibonacci sequences and Penrose tilings.
Contribution
It analyzes the impact of isomorphism choices on hierarchical structures and their matching rules, providing insights into structural equivalences.
Findings
Different isomorphism definitions influence structure classification
Matching rules depend on the chosen isomorphism criteria
Hierarchical structures exhibit varied properties under different isomorphism notions
Abstract
We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to matching rules for such structures.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Cellular Automata and Applications · semigroups and automata theory
