On the dimension of arcs in mixed labyrinth fractals

Autor:	Damir Vukicevic, Ligia L. Cristea
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Arc (geometry) Pure mathematics Box counting Fractal Property (philosophy) Construction method Dimension (vector space) FOS: Mathematics Dynamical Systems (math.DS) Mathematics - Dynamical Systems Unit square Mathematics
Popis:	Mixed labyrinth fractals are dendrites in the unit square introduced by Cristea and Steinsky. They were studied recently by Cristea and Leobacher with respect to the lengths of arcs in the fractals. In this article we first give a construction method for mixed labyrinth fractals with the property that all arcs in the fractal have box counting dimension 2. Subsequently, we show how a certain family of patterns can provide a mixed labyrinth fractal of any box counting dimension between 1 and 2, which also coincides with the box-counting dimension of the arc between any two distinct points of the fractal. Finally, we show how the results can be extended to a more general setting. 14 pages, 8 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1e7ba0063fc736d6f862f13936268a1 http://arxiv.org/abs/2103.07468 Zobrazit plný text záznamu