About Fibonacci trees. II -- generalized Fibonacci trees

TL;DR

This paper investigates properties of generalized Fibonacci trees rooted at black nodes in hyperbolic plane tilings, revealing new but comparable properties to those rooted at white nodes, extending previous work on Fibonacci trees.

Contribution

It extends prior research by analyzing how tree properties change when rooted at black nodes in hyperbolic tilings, uncovering new properties of these generalized Fibonacci trees.

Findings

New properties emerge for trees rooted at black nodes

Properties are no more complex than those rooted at white nodes

Extension of previous Fibonacci tree analysis

Abstract

In this second paper, we look at the following question: are the properties of the trees associated to the tilings $\{p,4\}$ and $\{p$+$2,3\}$ of the hyperbolic plane still true if we consider a finitely generated tree by the same rules but rooted at a black node? The direct answer is no, but new properties arise, no more complex than in the case of a tree rooted at a white node, and worth of interest. The present paper is an extension of the previous paper: arXiv:1904.12135.