Computers are really rather good at graphics. In fact, some kinds of graphics, such as fractals, would effectively be impossible to create in any other way. Computers have turned three-dimensional graphics from a time-draining nightmare into a relatively pleasant exercise with (often) superb results. And of course computers make it quite simple to animate graphics, which is where the special effects industry makes its money.

I am particularly fascinated by fractals; these are intriguing graphical representations of figures with a fractional dimension. They are created by recursive algorithms, algorithms which fold in on themselves infinitely (although, in practice, a fractal image generator must stop eventually).

One of the most fascinating fractals, to me, is the Sierpinksi Triangle. This isn't because it's particularly attractive (although it is far from ugly), but rather because it seems to crop up in all sorts of unlikely places -- for example, it is strongly linked to Pascal's Triangle, to cellular automata, and even to the classic "Towers of Hanoi" game.

Michael Barnsley devised a way of producing the Sierpinski triangle via a random process, which he called "The Chaos Game" (perhaps not a great name, actually, because the Sierpinksi Triangle isn't exactly chaotic and the process -- when executed manually -- isn't particularly entertaining, unless you are easily entertained!).

Steven Pettit and I came up with a modification to the Chaos Game (well, he thought of a way to modify it, and I modified his modification, and we went round the loop a couple of times until we were both more or less happy with it), which allowed us to produce a staggering range of basically new fractals, very simply indeed. We call our version of the Chaos Game the "Sierpinsky-Barnsley-Pettit-Heathfield" algorithm, for obvious reasons.