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

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

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