The Barnsley fern

So I am getting into my masters again. Which means I have lots of time to distract myself with pointless side projects. Hence we are delving again into the wonderful world of fractals. This time the fractals is called the Barnsley Fern. It's also a very famous fractal (as far as fractals can be famous. I don't think its famous like Tom Cruise. But how could a lowly mathematical object compete with the crown prince of Scientology).

The fractal, unsurprisingly, looks like a fern plant, or rather a leaf of a fern. Like many fractals it is made up of smaller versions of itself that have been scaled and rotated. It is also an infinitely complex object. If you had the computational power then in theory you could zoom into any part of it and find infinitely many copies of itself.

So here it is. It is set to keep drawing in more detail. To start it from scratch again click the redraw button.

This fractal was discovered by Michael Barnsley who was really into fractals. It is an example of a Iterated Function System(IFS). The interesting thing about it (which you can see in the animation) is that it is drawn one point at a time, and that how this point moves around is randomly chosen. But never the less it always draws the same picture. The Wikipedia article has a reasonably detailed explanation of how it is constructed (which really is simple). Check it out if you are interested.