Fractals Created From Nonaffine Functions And Predicting Attractor Parameters Using Neural Networks

dc.contributor.advisorDemers, Matthew
dc.contributor.authorGraham, Liam
dc.date.accessioned2020-08-14T13:14:58Z
dc.date.available2020-08-14T13:14:58Z
dc.date.copyright2020-08
dc.date.created2020-08-10
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.grantorUniversity of Guelphen_US
dc.degree.nameMaster of Scienceen_US
dc.degree.programmeMathematics and Statisticsen_US
dc.description.abstractFractals have a wide variety of applications in industries such as architecture and video games, as well as in research fields including soil mechanics and antenna design, amongst others. Finite collections of contractive set-valued affine functions, called iterated function systems (IFSs), have been shown to possess unique, globally attractive fixed points, termed attractors. These attractors often display fractal features. In this thesis we extend the theory of IFSs to include functions with bounded derivatives, and piecewise functions, both of which produce interesting results. Piecewise IFSs also allow for the development of fractal splicing. Additionally, we approximate a solution to a long-standing fractal inverse problem: Given the image of an attractor, what are the parameters of the IFS that produced it? We make use of neural networks to approximate this mapping.en_US
dc.description.sponsorshipQueen Elizabeth II Scholarship
dc.identifier.urihttps://hdl.handle.net/10214/18136
dc.language.isoenen_US
dc.publisherUniversity of Guelphen_US
dc.rights.licenseAll items in the Atrium are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectNon-affineen_US
dc.subjectFractalen_US
dc.subjectNonaffineen_US
dc.subjectNeural Networken_US
dc.subjectIterated Function Systemen_US
dc.subjectMachine Learningen_US
dc.subjectInverse Problemen_US
dc.subjectAttractoren_US
dc.subjectIFSen_US
dc.titleFractals Created From Nonaffine Functions And Predicting Attractor Parameters Using Neural Networksen_US
dc.typeThesisen_US

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