Dimensions of Self-Similar Fractals
Electronic Theses and Dissertations
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- abstract
- We investigate the topological, similarity and Hausdorff dimensions of self-similar fractals that are the invariant sets of iterated function systems. We start with the Contraction Mapping Theorem, which will give us a constructive method in which to find fractals using iterated function systems. We then define the Hausdorff metric in order to use the Contraction Mapping Theorem to prove that each iterated function system has a unique invariant set.
- subject
- dimension
- fractals
- iterated function systems
- math
- self-similar
- contributor
- Raynor, Sarah (committee chair)
- Parsley, Jason (committee member)
- date
- 2011-07-14T20:35:13Z (accessioned)
- 2011-07-14T20:35:13Z (available)
- 2011 (issued)
- degree
- Mathematics (discipline)
- identifier
- http://hdl.handle.net/10339/33433 (uri)
- language
- en (iso)
- publisher
- Wake Forest University
- title
- Dimensions of Self-Similar Fractals
- type
- Thesis