Mandelbrot remembered

Like many other people, I first saw the Mandelbrot Set in an issue of Scientific American in 1985. Before long I had written a program in BBC BASIC to perform the computation, and set my BBC Micro’s 2MHz 6502 churning away. Because it took so long to render an image — even at the Beeb’s meager 256x160 resolution in 8 non-blinking colors — I made the code preview by rendering every 16th pixel, then every 8th, and then finally fill in all the points. As well as Mandelbrot and Julia sets, I experimented a lot with Lindenmayer systems and generation of realistic-looking plants.

About a year later I upgraded to an Atari ST, with an 8MHz 68000 and the ability to handle 320x200 resolution in 16 colors. I had Computer Concepts' FaST BASIC, a version of BBC BASIC on a cartridge for the ST, and soon had fractals rendering on the Atari. I built a fairly elaborate menu and dialog system for adjusting parameters, and added mouse-based selection and zooming. Rendering speed was improved, but it still took a few minutes to put together a complete image.

The trend continued over the next decade: every time I got access to a newer and faster computer, one of the first things I would do would be to see how quickly it could draw fractals. This continued until the mid 90s, at which point I could move my mouse around the Mandelbrot set and see the corresponding Julia sets drawn in real time.

By then, fractal imagery had become commonplace on album covers and posters. My fascination waned. Yet Benoît Mandelbrot’s influence stayed with me; his fractal geometry had changed my view of the world. One single simple equation, simple enough for a teenager to understand — and yet, hidden inside it was infinite complexity. Simple iteration could generate images that looked like objects from the natural world. Entire universes could be encoded in a tiny algorithm, if you were clever enough.