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    Discussion and Application of Geometrically and Statistically Self-Similar Fractals

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    1995_WeberM_THS_000371.pdf (1.351Mb)
    Author
    Weber, Marvin
    Advisor
    Marie Vanisko; Anthony Szpilka; Philip Rose
    Date of Issue
    1995-04-01
    Metadata
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    URI
    https://scholars.carroll.edu/handle/20.500.12647/3465
    Title
    Discussion and Application of Geometrically and Statistically Self-Similar Fractals
    Type
    thesis
    Abstract
    This paper will present examples of fractal geometry with their respective techniques of analysis in order to illustrate the foundations for a quantitative study of the natural world. The first section studies dimension, both self-similar measure and Hausdorff-Besicovitch measure, emphasizing the idea of dimension as a measure rather than as a number of degrees of freedom. The second section presents random, statistically self-similar fractals. A topologically one-dimensional construction found in fair games of chance leads to the Levy flight, a topologically two-dimensional example that gives a model for the distribution of galaxies as viewed from Earth.
    Degree Awarded
    Bachelor's
    Semester
    Spring
    Department
    Mathematics, Engineering & Computer Science
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