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Fractals are interesting mathematical objects with a special behaviour in a complex-plane [Re, Im], depending on their initial position ( location). Visualised in popular media, typically as shapes with infinite dimensionality that exhibit a sort of self-similarity. Well-known fractal sets include the named Mandelbrot set, Julia sets, and Phoenix sets. Tree-like fractal drawings are also common.

Fractals are shapes that are self-similar.
https://stackru.com/images/2adbe4199ad166b1e3ceb96785aba8836996f1df.gif
Their infinite-dimensionality could be best viewed in animated computer simulations.

Fractal sets such as the Mandelbrot set, Julia sets, and Phoenix sets are commonly used for a fast, approximate (iterative) method of how to determine a point's membership in such a set in a complex-plane [Re, Im]. For example, if the absolute value of an iterative complex function (defining the Mandelbrot, or another set), the module, never grows beyond a given treshold, then the original point in complex-plane [Re, Im], the argument of the complex-function, is considered a member of the set.

Image presented by **flashliquid Fractal trees - drawings that resemble trees in nature can be drawn in high detail with recursive algorithms.