A Formal Treatment of Deterministic Fractals
نویسنده
چکیده
We explore in depth the theory behind deterministic fractals by investigat ing transformations on metric spaces and the contraction mapping theorem. In doing so we introduce the notion of the Hausdorff distance metric and its connection to the space of fractals. In order to understand how deterministic fractals are generated, we develop the concept of an iterated function system (IFS) and what it means for these fractals to be an attractor of the IFS. Fi nally, we give creedance to our notion of fractals as objects having fractional dimension, by introducing a simplified version of the Hausdorff Dimension.
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