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There are many known fractals that exist such as Mandelbrot, Cantor set, or the Koch curve, Sierpinski Triangle. What I am curious about, is how one could go about creating their own, unique fractal formula, and more importantly, how to prove that that it is in fact a true fractal.

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  • $\begingroup$ I do not know if this could be helpful, but just in case: you can start from something simple, L-Systems have rules that let you generate a fractalic structure, if you follow the rules then the result is a proven fractal structure. You can define which combination of rules you want to apply, so you can create your own L-System fractal. en.wikipedia.org/wiki/L-system $\endgroup$
    – iadvd
    Commented Mar 25, 2016 at 1:22

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