Geometry of Self-Similar Sets

(ABSTRACT) This paper examines self-similar sets and some of their properties, including the natural equivalence relation found in bilipschitz equivalence. Both dimension and preservation of paths are determined to be invariant under this equivalence. Also, sophisticated techniques, one involving the use of directed graphs, show the equivalence of two spaces. Acknowledgments I am grateful for the support and encouragement of my thesis advisor, Dr. Peter Haskell, who patiently, but firmly, directed my progress, bolstered my confidence, and helped bring my research and study skills to a higher level. My sincere appreciation also extends to Dr. Martin Day and Dr. Jim Thomson, members of my Masters Thesis Committee, for their time and effort in reviewing this work. ii