Strange attractors

Not to trump my colleague at chunk 34 of the Processing Book we are busily writing, but how does one explain an attractor, exactly?

In an iterated function system, particularly the random iteration algorithm, you pick a point, any point (nothing up the sleeve) and watch as it magically gets sucked into this attractor. Then the point hops around the attractor forever, apparently randomly moving about, but otherwise very nicely confined and constrained.

We don't tend to plot the first 10 iterations or so. This seems rather arbitrary, but I've not yet found a good explanation for how we decide when to start plotting.

What's the simplest attractor you could have? f(x) = 0? Ah, so f(0) = 0 is a fixed point of this system. And, f(x) = x has all points as fixed points. So we can explain that for some systems the set of fixed points has an interesting shape. Also that after a while we can remain on that shape, if we start out close enough to it to get sucked in by its 'gravitational pull'. What would that look like?

Pendulum? Not very interesting - its fixed point must be its bottom point. But it's a helpful analogy for thinking about attractors as fixed points, which is what IFSs are, except that they are sets of points. I don't want to get too mathematical.

Could do the Cantor set, I suppose, or an IFS to draw a line or a square or some such thing. The former is probably too abstract. The latter is visually uninteresting, but at least you can plainly see the attractor.

Hmm... more reading required.

Mass writing about processing

Okay, so this blog is about writing a bit of a book on the Processing environment. Quite nice it is too. The IDE is not great, although you can use an external one.

The great thing is that you can drop in Java code - it's Java underneath - and start drawing pictures within minutes. This is like BASIC used to be. Drawing lines and circles and what have you, sticking them in loops, changing the colours and widths of lines, all that fun stuff, without ever writing a paint method. But lots more, because you have all that Java power at your disposal and because they've thought about all the useful things you might like to do, like change transparency, or rotate and so on.

It looks like it will be fun. I have a mind to write something about Iterated Function Systems, taking me back to my days drawing fractals out of Barnsley's Fractals Everywhere book. It has not taken long to write my first attempts at that. Now I need to turn it into something accessible and fun to experiment with.

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I am getting to the point where I can't read those captcha things, and tried the audio.

I thought I'd dropped into an episode of Twin Peaks. There were dwarves break dancing. A leering man tapped me on the shoulder and said something backwards, before dancing tip toe out of the room. A strangely blue girl lay on my bed. Doves flew in my face and somebody spat a cherry pip at me.

Apparently this is how one starts a blog.