Triangular labyrinth fractals

About the paper

coauthor Ligia-Loreta Cristea
language English
published in Fractals, 27, No. 08 (2019)
page 1950131
DOI 10.1142/S0218348X19501317
supported by FWF, project P28991-N35

Abstract

We define and study a class of fractal dendrites called triangular labyrinth fractals. For the construction we use triangular labyrinth pattern systems, consisting of two triangular patterns: a white and a yellow one. Correspondingly, we have two fractals: a white and a yellow one. The fractals studied here are self-similar, and fit into the framework of graph directed constructions. The main results consist in showing how special families of triangular labyrinth patterns systems, which are defined based on some shape features, can generate exactly three types of dendrites: labyrinth fractals where all non-trivial arcs have infinite length, fractals where all non-trivial arcs have finite length, or fractals where the only arcs of finite lengths are line segments parallel to a certain direction. We also study the existence of tangents to arcs. The article is inspired by research done on labyrinth fractals in the unit square that have been studied during the last decade. In the triangular case, due to the geometry of triangular shapes, some new techniques and ideas are necessary in order to obtain the results.

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Links

Fractals
Austrian Science Foundation (FWF)
Homepage of the project P28991