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Set Inversion Fractals

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dc.contributor.advisor Kunze, Herb Boreland, Bryson 2016-08-25T15:38:08Z 2016-08-25T15:38:08Z 2016-08 2016-08-09 2016-08-25
dc.description.abstract In 2000, Frame and Cogevina introduced a method for constructing fractals using circle inversion maps. The literature focuses on the graphical aspect of such fractals, without presenting a careful development of the underlying mathematical framework. In this thesis, we present such a framework, making a strong connection to iterated function systems (IFS) theory. Our final result establishes that the set valued system of circle inversion maps induced by a collection of possibly overlapping circles in the plane has a unique set attractor. We then establish a similar mathematical framework in the setting of non-touching star-shaped sets. We present graphical examples for both settings using the chaos game. Finally, fractals literature develops the well-known concept of local iterated function systems with grey-level maps, with applications to image processing. We follow this path to establish a framework that uses local circle inversion maps as the functions. We demonstrate the results with examples. en_US
dc.description.sponsorship Ontario Graduate Scholarship en_US
dc.language.iso en en_US
dc.subject Fractals en_US
dc.subject Circle Inversion en_US
dc.subject Star-Shaped Sets en_US
dc.subject Signal Approximation en_US
dc.subject Banach's Fixed Point Theorem en_US
dc.subject Iterated Function Systems en_US
dc.subject Grey-Level Maps en_US
dc.title Set Inversion Fractals en_US
dc.type Thesis en_US Mathematics and Statistics en_US Master of Science en_US Department of Mathematics and Statistics en_US
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