Fractals and self-similarity

From the original patent application of the original “fractal” vise

Objects with a fractional Hausdorff dimension, AFAICT. For some equivocation on this theme, see wikipedia.

Iterated function systems

Connection to design grammars.

Fun fact: there is a fractal renderer built into GIMP.

Mandelbrot sets I guess


Non-local derivatives

See fractional derivatives.

Long memory time series

See, for example, fractional brownian motion, long memory time series.

In nature

Pattern formation in nature often looks fractal to some approximation, or at some range of scales.

Horse lung

Starfish of infinite surface area.


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