Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension

Manuel  Fernández-Martínez; Miguel Ángel López  Guerrero

doi:10.3934/dcdss.2015.8.1129

Article Contents

2015, Volume 8, Issue 6: 1129-1137. Doi: 10.3934/dcdss.2015.8.1129

This issue Previous Article Theoretical properties of fractal dimensions for fractal structures Next Article Dynamic systems based on preference graph and distance

Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension

1.
University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, Coronel López Peña Street, w/n, 30720 Santiago de la Ribera, Murcia
2.
Department of Mathematics at University of Castilla-La Mancha, Campus Universitario de Cuenca, 16071 Cuenca

Received: May 2015

Revised: September 2015

Published: December 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we explain how to generate adequate pre-fractals in order to properly approximate attractors of iterated function systems on the real line within a priori known Hausdorff dimension. To deal with, we have applied the classical Moran's Theorem, so we have been focused on non-overlapping strict self-similar sets. This involves a quite significant hypothesis: the so-called open set condition. The main theoretical result contributed in this paper becomes quite interesting from a computational point of view, since in such a context, there is always a maximum level (of the natural fractal structure we apply in this work) that may be achieved.

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Mathematics Subject Classification: Primary: 28A80; Secondary: 37F35, 54E99.

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