A fractal is a term to describing a self-similiar figure. Like a cauliflower, the form is self-similiar and repeats itself multiple times, that way Nature is able to form complex structures based on one rule-set, which is applied on a smaller scale again. Another good example is the fern. Fractals for me is the "Beauty of the Mathematical World", and all manifested forms use its functionality.
More examples follow ...
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