Fractals: A World of Artful Math

Benoit Mandelbrot (1924-2010) was a mathematician, coiner of the word "fractal," and the most important figure in describing fractals. When asked to summarize them in seven words, he said, "Beautiful, damn hard, increasingly useful. That's fractals." (1:42)

Fractals are beautiful in their apparently infinite complexity that is derived from relatively simple equations. Not only are they useful for a variety of purposes, they are also pleasing to the eye.

(Right-click and view image to see full size.)
Edwin Abbott Abbott used the simple concept of dimensions to create Flatland (1884), a short story that explores several different worlds (particularly the titular two dimensional one) and how they relate to each other. Similarly, the simple concept of fractals is used to create amazing images that express math in an artistic way.

Fractals also provide another example of the combination of art and technology. Math alone is not enough to generate fractals; computers are necessary to create the images themselves, which can't be created by the human hand.  Mandelbrot's access to computers in the late 70s and the 80s were critical to his discovering of fractals.

"Parade" by C-91. http://c-91.deviantart.com/art/Parade-325037384 for the full size.

In this work, the artist used computers and fractals to achieve a level of detail not possible with traditional art mediums. As technology advances, new art techniques will become possible, ones that we might not even be able to imagine presently.

 

Finally, here is a song about the Mandelbrot set, by the great Jonathan Coulton. It is completely accurate, including the part about day-glo pterodactyls.

Sources

Abbott, Edwin A. Flatland: A Romance of Many Dimensions. Princeton: Princeton UP, 1991. Web. http://www.ibiblio.org/eldritch/eaa/FL.HTM

C-91. "Parade." DeviantArt. DeviantArt. Web. 10 Apr. 2016. http://c-91.deviantart.com/art/Parade-325037384

Foellmi. "Jonathan Coulton Mandelbrot Set HD." YouTube. YouTube, 2009. Web. 10 Apr. 2016. 

"How To Trade The Fractal Indicator." Winners Edge Trading. Web. 10 Apr. 2016. http://winnersedgetrading.com/how-to-trade-the-fractal-indicator/

ImprobableResearch. "Improbable Research Collection #135: Benoit Mandelbrot's 24/7 Lecture on Fractals." YouTube. YouTube, 2013. Web. 10 Apr. 2016.

Weisstein, Eric W. "Mandelbrot Set." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/MandelbrotSet.html