Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 17.2.2015 |
| Speaker: | Kevin Hare, Department of Pure Mathematics, The University of Waterloo |
| Title: | Iterated Function Systems |
| Abstract: | Many historical examples of fractals, such as the Cantor Set (Smith, 1874, Cantor 1883), Sierpinski's Triangle (Cosmati 13th Century, Sierpinski, 1915) and the Koch curve (Koch 1904) are special cases of a more general construction, called Iterated Function Systems (IFS). Let $f_1, f_2, \dots, f_n$ be a set of contraction maps. We define the IFS based on $f_1, f_2, \dots, f_n$ as the unique non-trivial compact operator $K$ such that $K = \cup f_i(K)$. In this talk we consider the very simple family of contraction maps, $f_1(x,y) = (\mu x -1, \lambda x - 1)$ and $f_2(x,y) = (\mu x + 1, \lambda x + 1)$ where $0 \leq \lambda, \mu < 1$. We will investigate how properties of this IFS vary as $\mu$ and $\lambda$ vary, demonstrating a surprisingly rich structure. |
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