Browsing by Author "Roinestad, Kristine A."

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    Geometry of Fractal Squares
    Roinestad, Kristine A. (Virginia Tech, 2010-04-12)
    This paper will examine analogues of Cantor sets, called fractal squares, and some of the geometric ways in which fractal squares raise issues not raised by Cantor sets. Also discussed will be a technique using directed graphs to prove bilipschitz equivalence of two fractal squares.
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    Geometry of Self-Similar Sets
    Roinestad, Kristine A. (Virginia Tech, 2007-05-08)
    This paper examines self-similar sets and some of their properties, including the natural equivalence relation found in bilipschitz equivalence. Both dimension and preservation of paths are determined to be invariant under this equivalence. Also, sophisticated techniques, one involving the use of directed graphs, show the equivalence of two spaces.