Mink Machine

So long Mandelbrot and thanks for all the fractals

The mathematician Benoit Mandelbrot died today of pancreatic cancer at the age of 85. I guess most people don’t have a clue who he is, but he used to be one of my unlikely childhood heroes.

Often called the “father of fractals”, Mandelbrot was one of the most well-known pioneers into this abstract field of mathematics. He studied the works of Gaston Julia among others and coined the term “fractal” for certain geometric shapes that displayed certain unique properties. Fractal geometry had already been studied by Leibniz back in the 17th century, but Mandelbrot brought this obscure backwater mathematics out into the open. In 1980 he saw the first visualization of what would later be named the Mandelbrot set.

Typical behavior of a fractal geometry is that more intricate details are shown the more it is zoomed in. If you are unfamiliar with the Mandelbrot set, have a look at this video.

The colours are simply representing certain numbers in the complex plane. Think of it the same way as the images of space we see from the telescopes where the colours are vividly enhanced.

Since the Mandelbrot set and its friends were visually appealing and mathematically interesting, it also became popular among young computer enthusiasts in the early days. I coded my first fractal in the early nineties using assembly language and later made a Java version of the Julia set:

Julia morph Morphing Julia set. Run simulation.

9 comments

  • avatar
    Mandus
    18 Oct, 2010

    Had a look at the Julia-applet, and it ran in 250 fps on my computer. 10 years and a lot of MHz later. :)

  • avatar
    18 Oct, 2010

    Hehe, I get approx 170 fps here. Maybe it’s time to code a fullscreen version in 3D? :)

  • avatar
    Mandus
    29 Oct, 2010

    Soooo… my computer is better than yours. Wop wop!

  • avatar
    29 Oct, 2010

    Enjoy it while it lasts. :)

  • avatar
    bollman
    13 Nov, 2010

    On my spanking new MacBook Air 11″ I get about 150fps but on my Mac Pro I only get about 80. Something is rotten in the state of Java…

  • avatar
    Mandus
    18 Nov, 2010

    290 now, my computer is evolving! \o/

  • avatar
    bollman
    01 Feb, 2011

    Well, now Google Labs has made good use of Google Maps ;)
    http://juliamap.googlelabs.com

  • avatar
    01 Feb, 2011

    Brilliant! I wonder if we can use “get directions” to find the way to a particular set of numbers?

  • avatar
    bollman
    02 Feb, 2011

    Note: it works on iPhone/iPad.
    On an iPad, max 1 million FLOPs
    On an iPhone 3Gs, slightly less ;)

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