Roinestad, Kristine A.2014-03-142014-03-142007-05-08etd-05112007-130841http://hdl.handle.net/10919/32581This 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.In CopyrightSelf-SimilarityCantor SetsBilipschitz EquivalenceThesishttp://scholar.lib.vt.edu/theses/available/etd-05112007-130841/