Source code for the applet, and for some other related programs. I wrote these as illustrations for a talk.
This applet requires Java version 1.3 or later. You can download version 1.5 for free from www.java.com. If anybody finds the applet works on an older version let me know.
> What does one do with a Mandelbrot set?
You click on a bit that looks interesting. Repeat every few minutes. When you reach the limit of the numerical accuracy, reload and start again. It's very soothing. There are lots and lots of patterns in it if you look carefully. For example, the "Y" shape at the top is a 3-armed spiral which is part of a sequence of spirals with 2 arms, 3 arms, 4 arms, etc. The 2-armed spiral is difficult to recognise because it is a straight line. The 3-armed spiral is also the start of a sequence of spirals with 3 arms, 5 arms, 7 arms, etc. Also, these two sequences are the first two of a sequence of sequences. And every spiral has a sequence of little beetles down each arm. On the arm which joins the spiral to the main set, the beetles point towards the middle of the spiral, and on the other arms they point away from the middle. Between every pair of beetles on an arm you can find another smaller beetle. And that's just the tip of the iceberg. Off you go!