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I have a question about classifying a few fractals I've been programming.

I understand that there are types of fractals like L-systems (Barnsley's Fern, Fractal plant, ...), IFS systems (Sierpinski's gasket, Fractal flames, ...).

I'm a bit confused where to classify the Mandelbrot set and the Julia sets, do they belong to any category of fractals?

Same thing with Koch snowflake, can I classify it under L-systems?

I'm having trouble finding a complete overview on types of fractals, however there are many examples of individual fractals on wikipedia and such..

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The categories that you mention (Iterated Function Systems, or IFSs, and L-Systems) are tools for the construction of certain types of sets. Thus, you might try to classify your fractal images via the tools you used to construct them. You should understand, however, that there will probably be quite a bit of overlap between the categories. The Sierpinski triangle and many other self-similar sets can be described via an IFS or an L-system.

The two-dimensional Koch Snowflake, that you ask about, can be constructed via an IFS, as in this answer. It's fractal boundary, can be described via L-System and a portion of that boundary can be described via an IFS.

Julia sets and the Mandelbrot set live more properly in the context of complex dynamics. One can certainly attempt to analyze them with fractal tools, like Hausdorff dimension, but this is somewhat more difficult.

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