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Self-similarity: Revision history


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  • curprev 18:2518:25, 9 October 2019 Hyacinth talk contribs 12,877 bytes −446 {{Quote|If parts of a figure are small replicas of the whole, then the figure is called ''self-similar''....A figure is ''strictly self-similar'' if the figure can be decomposed into parts which are exact replicas of the whole. Any arbitrary part contains an exact replica of the whole figure.<ref>Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar; Maletsky, Evan; Perciante, Terry; and Yunker, Lee (1991). ''Fractals for the Classroom: Strategic Activities Volume One'', p.21. Springer-Verlag, N undo

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  • curprev 03:5603:56, 3 October 2019 Hyacinth talk contribs 13,353 bytes +357 top: {{Quote|In order to give an operational meaning to the property of self-similarity, we are necessarily restricted to dealing with finite approximations of the limit figure. This is done using the method which we will call box self-similarity where measurements are made on finite stages of the figure using grids of various sizes.<ref name="Classroom"/>}} undo
  • curprev 03:5203:52, 3 October 2019 Hyacinth talk contribs 12,996 bytes +1,079 top: {{Quote|One approach to understanding the notion of self-similarity involves the ability to apply an iterative rule in a geometric setting....after infinitely many iterations....A striking feature of the Sierpinski triangle is its strict self-similarity. The completed Sierpinski triangle naturally decomposes into three triangular parts, an upper portion and two lower portions. Each of these parts is an exact replica of the whole original figure. Likewise, each of these parts itself can undo

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