Whether you understand them or not, the visuals of the Mandelbrot set, and most other fractals, are bloody amazing to watch! But what makes them tick? What makes those shapes and colours happen? Depending on your math literacy, this can be anywhere from difficult to impossible to understand, but regardless of that, the images are still there to be enjoyed.
Mandelbrot detail (Wikipedia)
I flatter myself by saying to anyone who is interested (which is usually just me) that I feel I’m somewhere halfway between not getting it, and having something of a feeble grasp of the apparent magic. I’ve absorbed enough to, back in the early Nineties, make a working — if, to be honest, rather unimpressive — Mandelbrot renderer on my computer (a Commodore Amiga 1200) in some obscure version of the programming language Pascal. My breakthrough came when reading the appendix to Arthur C. Clarke’s 1990 novel “The Ghost From The Grand Banks”, in which fractals play an appreciable part, where he details the interplay between real and imaginary numbers to the point where I managed to break it down to a working algorithm for my Mandelbrot renderer.
But having the algorithm worked out, I still find it pretty darn hard to visualize in my mind what the heck is happening when you start crunching the numbers. It’s fascinating, but almost incomprehensible, and I’ll take any explanation that will make it easier to wrap my head around it.
Fortunately the Internet is full of helpful people with ideas for explaining seemingly inexplicable things to people like myself. Such as this highly inspiring and entertaining visual walk-through by Mathologer of how the maths of the Mandelbrot set works. Put on your science goggles and press Play!
Incidentally, if you’d like a cute (and bloody clever) redhead to explain the basics of the Mandelbrot set for you, then look no further, because Numberphile‘s Dr Holly Krieger delivers.