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What are fractals?

What are fractals? Here are some definitions.

Noun
  1. plural of fractal
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All of these elements are combined into seemingly aleatory compositions that, like fractals, operate on several scales at once.
For example, we observe the presence of coexisting lipid phases and unstable domain growth that results in patterns such as fractals.
The approach of this paper was originally developed in to study the Hausdorff measure of certain parameterized families of fractals.
Mathematicians can use similar algorithms to generate fractals and other forms.
Many natural chaotic systems form fractals in the patterns that record the process.
This requires fractals to be given dimensions that are not whole numbers but fractions.

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