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I have an old Spanish CG book that calls Perlin Noise a "fractal structure". After reading this I couldn't deny it or confirm it. Is it a fractal structure? What would it Hausdorff dimension be?

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Since there has been no reply, can you explain what you mean by "fractal structure". I suppose that if you think about it in terms of increasingly becoming less noisy, it may be a fractal. –  picakhu Dec 19 '10 at 21:21
    
I mean self-similar on multiple scales. Is this fractal noise? –  omgzor Dec 20 '10 at 20:50
    
it is statistically self similar. That is a type of fractal. –  quanta Apr 10 '11 at 12:13

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You can consider two types of fractals: deterministic of an iterative structure (like a Kantor's set) and stochastic which is self-similar in law. If a Perlin noise is a stochastic noise? Then you should verify if there exist a rescaling such that it preserves the distribution law.

On the other hand, the term "fractal" is not formalized, so you can use it for any "self-similarity".

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