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Fractals deal with special sets that exhibit complicated patterns in every scale. Fractal sets usually have a Hausdorff dimension different from its topological dimension. Examples include Julia sets, the Sierpinski triangle, the Cantor set. Fractals naturally appear in dynamical system, such as iterations in the complex plane, or as strange attractors to continuous dynamical systems, (see Lorentz attractor).
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Julia sets using other fields
I hope I am forgiven for my noob question. But, does it make sense to think of Julia sets using other fields? More precisely I would like to think of fields in which closed and bounded isn't necessari …
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Fractal questions: Weierstraß-Mandelbrot
My question is whether there are nowhere differentiable continuous functions (between real numbers) whose graphs are not fractals? … (My reference suggests that the suggested definition was the former definition by Mandelbrot, and then this definition was changed as Mandelbrot fractals don't follow this definition.) …