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Rendering and magnification of fractals using iterated functionsystems

Reuter, Laurie Beth Hodges (1987) Rendering and magnification of fractals using iterated functionsystems. PhD.

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Thesis Georgia Institute of Technology, USA SUMMARY Fractal sets do not simplify geometrically when magnified. As viewing resolution is increased, so is the visible detail. Fractals have been found to be particularly useful for modeling the jagged and irregular geometry of typical natural objects. Thus they are important tools for geometric modeling in computer graphics.An iterated function system or IFS is a mathematical model which when realized by an iteration process generates a fractal set called the attractor of the IFS. An iterated function system has the property that its parameters can be chosen so that its attractor matches any specified shape with as much accuracy as is desired.This thesis addresses the rendering and magnification issues of producing computer generated images of fractals that have been obtained via iterated function systems. Two techniques for rendering IFS attractors are presented. The first, the measure rendering method, can be used to add texture to an image of a two-dimensional IFS attractor and produce images that display a high degree of realism. The second, the point history method, reveals details of the attractor according to the iterative process that generated it.A new two-phase magnification algorithm with several performance-enhancing variations is introduced. It produces magnified views of attractor subsections in far less time than previous methods. The solution to the magnification problem is dimension independent and preserves the properties of IFS attractors needed by the new rendering techniques.The Seurat software system is a complete interactive rendering system that incorporates the research results from this work. A discussion of its implementation and companion animation software in included.

Item Type: Thesis (PhD)
Language: English
Publisher: UMI
Date of graduation: 1 December 1987
Status: Published
Date Deposited: 02 Jun 2020 10:47
Last Modified: 02 Jun 2020 10:47

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