Date of Award

Spring 1995

Document Type

Thesis

Department

Mathematics, Engineering & Computer Science

First Advisor

Marie Vanisko

Second Advisor

Anthony Szpilka

Third Advisor

Philip Rose

Abstract

This paper will present examples of fractal geometry with their respective techniques of analysis in order to illustrate the foundations for a quantitative study of the natural world. The first section studies dimension, both self-similar measure and Hausdorff-Besicovitch measure, emphasizing the idea of dimension as a measure rather than as a number of degrees of freedom. The second section presents random, statistically self-similar fractals. A topologically one-dimensional construction found in fair games of chance leads to the Levy flight, a topologically two-dimensional example that gives a model for the distribution of galaxies as viewed from Earth.

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