Isomorphism of Hierarchical Structures

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.