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I'm interested in the topic of fractals, such as those created by the borders of the Mandelbrot and Julia sets.

My question is if there are other, not yet discovered fractal sets, which one could find by experimenting with the generation formulas (using a computer). I mean of course fractals which are substantially different in their appearance and "behaviour" than the ones which are already known.

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    Contrary to popular opinion, "fractal" does not have a rigorous mathematical definition.2012-01-28
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    Not all fractals are generated by formulas like the Mandelbrot set is. There are a LOT of fractally things. They come up all over the place; consider this interesting example: https://johncarlosbaez.wordpress.com/2011/12/11/the-beauty-of-roots/2012-01-28
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    @QiaochuYuan Is it possible to give it one?2012-04-19
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    @Peter: something something non-integer Hausdorff dimension something something?2012-04-19
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    @RahulNarain Planar Cantor-type sets have Hausdorff dimension anywhere between 0 and 2 (see the animation here http://www.usna.edu/MathDept/website/faculty/mdm/presentation/allca.gif ), and there is no reason to exclude the 1-dimensional set from this family. In fact, it's the most interesting member of the family from some points of view.2012-05-19
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    @Rahul: for starters, you'll have to work out what to put in the somethings to make that cover the Mandelbrot set. Both it and its boundary have dimension $2$.2012-10-19

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