Improved methods for calculating the multifractal spectrum for small data sets
| dc.contributor.author | Anderson, Leif, author | |
| dc.contributor.author | Eykholt, Richard, advisor | |
| dc.contributor.author | Robinson, Raymond Steve, committee member | |
| dc.contributor.author | Gelfand, Martin, committee member | |
| dc.contributor.author | Wu, Mingzhong, committee member | |
| dc.contributor.author | Shipman, Patrick, committee member | |
| dc.date.accessioned | 2007-01-03T06:41:00Z | |
| dc.date.available | 2007-01-03T06:41:00Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | There are multiple definitions for fractal dimension, and those definitions disagree. The multifractal spectrum provides a unifying framework for a broad family of definitions of dimension, but it requires large amounts of data to compute. We provide a description of the multifractal spectrum, one existing improvement that improves convergence for small data sets: the Extended Box Algorithm (EBA), and develop several further improvements: Local and Global Norm modifications to the EBA, the a-Norm, the Variable Box size Algorithm (VBA), and the Patchwork method. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Anderson_colostate_0053A_12288.pdf | |
| dc.identifier.uri | http://hdl.handle.net/10217/82579 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject | multifractal | |
| dc.title | Improved methods for calculating the multifractal spectrum for small data sets | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Physics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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