# American Institute of Mathematical Sciences

December  2015, 8(6): 1129-1137. doi: 10.3934/dcdss.2015.8.1129

## 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, Spain

Received  May 2015 Revised  September 2015 Published  December 2015

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.
Citation: Manuel Fernández-Martínez, Miguel Ángel López Guerrero. Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1129-1137. doi: 10.3934/dcdss.2015.8.1129
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