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SUMMARY:Graduate Student Colloquium: Matt McClinton
DESCRIPTION:Fractal Geometry and Non-Integer Dimensions\nMatt McClinton\nPhD Graduate Student\nUniversity of Wisconsin-Milwaukee \nPopularized in the 1980s\, fractals have become something of a household name. These fractal sets often demonstrate peculiar topological properties. One such property is the notion of a fractal dimension. Sets such as the Cantor set\, Sierpinski Gasket (SG)\, and the von Koch curve are traditionally visualized in 2D images. However\, these sets actually exist in-between dimensions 1 and 2! \nCertain fractals can be built using what is known as an Iterated Function System (IFS)\, and there is a powerful theorem stating that having an IFS representation of a fractal provides a simple means of determining the fractal dimension. I will begin by stating the IFS that generates the Sierpinski Gasket. There are two transformations on the Gasket to which creates the Level-n Stretched Sierpinski Gasket (SSG^n). I will demonstrate how one constructs the IFS for SSG^n\, as well as provide the highlights to a theorem in which I prove the fractal dimension of SSG^n.
URL:/math/event/graduate-student-colloquium-matt-mcclinton-2/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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