Nov 20

Fractal Day

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Tartan Fractal Art
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“A fractal is a way of seeing infinity.”

~ Benoit Mandelbrot (1924-2010), the "Father of Fractals"

Fractals are objects in which the same patterns occur again and again at different scales and sizes. In a perfect mathematical fractal – such as the famous Mandelbrot set – this “self-similarity” goes infinitely deep: each pattern is made up of smaller copies of itself, and those smaller copies are made up of smaller copies again, forever. Many natural phenomena are fractal to some degree - eroding coastlines, snowflake geometry, and can even be found in partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation. Fractals are ubiquitous in nature, but are also found in human pursuits, such as music, painting, architecture, and even stock market prices!

Benoit B.  Mandelbrot (1924 – 2010) was a Polish-born, French and American mathematician with broad interests and contributions in the practical sciences.

 

He is particularly recognized for his contribution to the field of fractal geometry, including coining the word "fractal", as well as for developing a theory of "roughness and self-similarity" in nature.   He referred to himself as a "fractalist."

A fractal is a natural phenomenon or mathematical set that exhibits a repeating pattern that displays the same at every scale - also known as expanding symmetry or evolving symmetry.  Fractals are not limited to geometric patterns, but can also describe processes in time.  

 

Fractal patterns have been studied and rendered in images, structures and sounds and are found in naturetechnology, art, and processes, such as chaos theory.

Phenomena known to have fractal features include:

Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the "Mandelbrot set" in 1979.   A Mandelbrot set is a series of images which exhibit an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications or "zooming in."

Mandelbrot set zoom videos are popular exercises in computer mathematical visualization.

 

This tartan, by designer Carol A.L. Martin, gives the impression of a pattern within a pattern, and the sense of peering into a moment of a Mandelbrot set zoom.

 

Click the fractal art of the Julia Set (a different application of the same formula as the Mandelbrot set) for an impressive video showing the correlation between the two.

Officially registered tartan graphics on this site courtesy of The Scottish Tartans Authority.  Other tartans from talented tartan artists may also be featured.

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