The Mandelbrot set is hard to explain mathematically without a bunch of jargon, but as simply as I can say it:
- It exists on the complex plane, so one axis is the real part of a complex number and the other is the imaginary part (the multiple of the square root of -1).
- It represents the boundary between which the following statement is true or false for a given complex number c:
- let an accumulator z = 0. If you set z to (z squared + c) an infinite number of times, you don’t get infinity as a result.
- As you magnify the boundary between true and false ever larger, you never lose detail; it has an infinite capacity for detail.
At a low level of detail, it looks like this:
Benoit Mandelbrot was a Polish born mathematictian, who moved to France as a child in the lead up to WWII and moved to America to study aeronautics at Caltech in the late ’40s. After bouncing between Europe and the US, Mandelbrot eventually ended up at IBM and spent 35 years there before becoming a professor at Yale late in life. He coined the term “fractal” to describe items like the Mandelbrot set that have different shape at the edge based on how closely they are measured. Fractal-like structures exist in nature in coastlines, mountains, romanesco broccoli, fern leaves, and things that move chaotically like the stock market.
“Mandelbrot Set” is also the first track on Huck’s 2008 self-titled album; this doesn’t have anything to do with the item itself, but it is a chance to remember singer/songwriter Scott Ricciuti, whose absence we still feel. You can hear the song here.