Fractals etc.

The death of Benoit Mandelbrot the other day brought back memories of my ZX Spectrum taking about half an hour to produce the famous "Mandelbrot set" and of how I would sit there fascinated watching it emerge line by line.  Now on my current computer it takes just a few seconds.  My other memory concerning his work was the answer to the question "How long is the coastline of Britain" - and it turns out that it's infinitely long.  It all depends on how detailed you want to be - the more detail you are prepared to accept, the longer it is, and as the amount of detail is infinite, so is the length.  Fascinating stuff he came up with, though I didn't understand a tenth of it.