Symmetry in Fractals

Fractals lead to a new notion of symmetry. Fractal is a mathematical name used to describe the patterns of scale-self similarity which occur nearly the same at different levels. To elaborate, it is used when a specific and detailed pattern is seen to repeat itself.

Fractals are different from other geometric figures for in fractals, even though one sees one-dimensional lengths doubled, the corresponding spatial content of the fractal scales by a power that is not necessarily double also or even an integer (this spatial content of the fractal scale is referred to in the video as mass, example given is the Sierpinski triangle). This power-exponents are called fractal dimensions or scale dimensions.

The general consensus is that theoretical fractals are infinitely self-similar, iterative and detailed mathematical constructs having fractal dimensions. There may not be an agreed upon definition, different kinds of examples and applications about this have been formulated and studied in great depth.

Reference: http://www.mdpi.com/journal/symmetry/special_issues/symmetry_fractals

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