Can someone explain me what is the difference between strictly and exactly self-similar fractals? What is the stronger possession and what are the examples for both types? Thanks in advance.
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As near as I can tell from a brief look at the book the OP cites, "strict" self similarity means you see similarity no matter where you look -- Addison gives the Sierpinski triangle as an example of strict self similarity and a spiral as an example that's self similar only at the center of the spiral but nowhere else -- while "exact" means you see an exact copy of the fractal at each point of self similarity, as opposed to something that merely has the same general appearance, which Addison calls "statistical" self similarity. All this is explained in the first few pages of the book, where the terms appear in boldface. Nothing there, though, is given with any mathematical rigor; whether rigorous definitions are given later, I can't say. (I was looking on googlebooks, which limits what's shown.)
Barry Cipra
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Thanks, just one question about strict self similarity: do these copies inside of fractal have to be exact copies or they can be in some way deformed like in Mandelbrot set? Does that mean that exact self similarity implies strict self similarity? – user121 May 03 '18 at 20:34
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@user121, again, Addison doesn't seem to give rigorous definitions, so I can't say exactly what "exactly" means. But I think that the example of the spiral shows exact self similarity at its center, so I am inclined to say that exact self similarity does not imply strict self similarity. However, Addison does say that his book is mainly (if not exclusively) interested in fractals that are strictly self similar. – Barry Cipra May 03 '18 at 20:43