Mandelbrot and his Fractals
by A. Richard Miller
visits since 110215; last updated 110303.

(This web page was the MMS "Extra Feature" for the second half of February 2011.)

Here, we'll look at another branch of science - mathematics - and we'll show you some wonderful 3D and 4D images.

Benoit Mandelbrot passed away this past October. Known as "the father of fractal geometry", he also pioneered in other significant areas. Wikipedia provides a good biography of this great mathematician, here.

Mandelbrot FractalOnce fractal images became popular in the early 1980s, they inspired some nice applications to generate them on our home computers. (We enjoy GNU XaoS; it can be installed from the Ubuntu Software Center.) As computers gained speed and storage, home fractals drew faster and became ever more beautiful, but most fractals remained two-dimensional like the one on the right.

Today, take a look at these wonderful 3D and 4D (that is, with time; animated) fractal images. To learn more, here's a history of the new fractals (along with more lovely images).

Mathematics can have strange interfaces with real life. Mandelbrot evolved his theory of fractals to counter Big Bang theorists, who argued that "without a Big Bang, the light from many more stars farther away would create a glowing sky." Mandelbrot's fractals provide a different explanation for the dark night sky that we observe in nature.

Mathematics also has strange interfaces with art. Consider these hybrid fractals, which are calculated based on an artist's cues.

Cheers from
--Dick and Jill Miller, Partners, MMS <>