About Fibonacci trees III: multiple Fibonacci trees

TL;DR

This paper explores the properties of Fibonacci trees related to hyperbolic plane tilings, examining effects of root placement, node rules, and digit representations, extending previous work on Fibonacci tree structures.

Contribution

It investigates how modifications in tree construction and representation affect Fibonacci tree properties, extending prior research with new variants and insights.

Findings

Properties of Fibonacci trees are sensitive to root placement and node rules.

Changing digit representations impacts the structure and properties of Fibonacci trees.

The study extends understanding of Fibonacci trees in hyperbolic tiling contexts.

Abstract

In this third paper, we revisit the question to which extent the properties of the trees associated to the tilings $\{p,4\}$ of the hyperbolic plane are still true if we consider a finitely generated tree by the same rules but rooted at a black node? What happens if, considering the same distinction between black and white nodes but changing the place of the black son in the rules. What happens if we change the representation of the numbers by another set of digits? We tackle all of these questions in the paper. The present paper is an extension of the previous papers arXiv:1904.12135 and arXiv:1907.04677.