Fractals as Fixed Points of Iterated Function Systems
نویسنده
چکیده
This paper discusses one method of producing fractals, namely that of iterated function systems. We first establish the tools of Hausdorff measure and Hausdorff dimension to analyze fractals, as well as some concepts in the theory of metric spaces. The latter allows us to prove the existence and uniqueness of fractals as fixed points of iterated function systems. We discuss the connection between Hausdorff dimension and iterated function systems, and then study an application of fractals as unique fixed points in dynamical systems theory.
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