Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension
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.
Keywords:
- Discrete mathematics
- Mathematical analysis
- Effective dimension
- Mathematics
- Packing dimension
- Dimension function
- Urysohn and completely Hausdorff spaces
- Hausdorff measure
- Hausdorff dimension
- Continuous functions on a compact Hausdorff space
- Topology
- Minkowski–Bouligand dimension
- Outer measure
- Pure mathematics
- Hausdorff distance
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