On Bi-Lipschitz classification of fractal cubes possessing one-point intersection property

TL;DR

This paper classifies fractal cubes of order 3 with one-point intersection property into isometric, bi-Lipschitz, dendrite, and non-dendrite classes, revealing the structure of their geometric relationships.

Contribution

It provides a complete classification of fractal cubes with specific intersection properties into isometric and bi-Lipschitz classes, including dendrites and non-dendrites.

Findings

105 isometric classes of fractal cubes identified

5 bi-Lipschitz classes of dendrites established

7 bi-Lipschitz classes of non-dendrites identified

Abstract

We show that there are 105 isometric classes of fractal cubes of order 3 with 7 copies possessing one-point intersection property which are subdivided to 5 bi-Lipschitz classes of dendrites and 7 bi-Lipschitz classes of non-dendrites