Supermixed labyrinth fractals

  • Ligia L. Cristea

    Karl-Franzens-Universität Graz, Austria
  • Gunther Leobacher

    Karl-Franzens-Universität Graz, Austria
Supermixed labyrinth fractals cover

A subscription is required to access this article.

Abstract

Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [3, 4], then in the mixed case [5, 6]. Supermixed fractals constitute a significant generalisation of mixed labyrinth fractals: each step of the iterative construction is done according to not just one labyrinth pattern, but possibly to several different patterns. In this paper we introduce and study supermixed labyrinth fractals and the corresponding prefractals, called supermixed labyrinth sets, with focus on the aspects that were previously studied for the self-similar and mixed case: topological properties and properties of the arcs between points in the fractal. The facts and formulæ found here extend results proven in the above mentioned cases. One of the main results is a sufficient condition for infinite length of arcs in mixed labyrinth fractals.

Cite this article

Ligia L. Cristea, Gunther Leobacher, Supermixed labyrinth fractals. J. Fractal Geom. 7 (2020), no. 2, pp. 183–218

DOI 10.4171/JFG/88