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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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".