My favorite is the Peter de Jong attractor, described here: http://paulbourke.net/fractals/peterdejong/

Here's a <canvas> version. Click and drag and release to re-seed the starting coordinates: http://jashkenas.s3.amazonaws.com/misc/deJong/deJong.html

Here's the annotated source code: http://jashkenas.s3.amazonaws.com/misc/deJong/docs/deJong.ht...

Edit: I've added a permalink button, so that you can link directly to interesting coordinates that you discover: http://jashkenas.s3.amazonaws.com/misc/deJong/deJong.html#59...