{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/33433"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/33433","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Dimensions of Self-Similar Fractals","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Glass, Melissa Ann"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011","date_published":"2011","updated_at":"2026-07-27T22:01:14Z","subjects":["dimension"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/33433","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Glass, Melissa Ann"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2011-07-14T20:35:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-07-14T20:35:13Z"]},{"key":"dc:date.issued","label":"Date","values":["2011"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["dimension"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/33433"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Dimensions of Self-Similar Fractals"]}]}],"canonical_facts":{"dc:creator":["Glass, Melissa Ann"],"dc:date.accessioned":["2011-07-14T20:35:13Z"],"dc:date.available":["2011-07-14T20:35:13Z"],"dc:date.issued":["2011"],"dc:description.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."],"dc:identifier.uri":["http://hdl.handle.net/10339/33433"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["dimension"],"dc:title":["Dimensions of Self-Similar Fractals"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:14Z"}