Follow that bird

Looking out at the sky as I write this: two or three kites up high, wheeling lazily; lower down, the occasional crow, then a pigeon that flaps frantically from one building to another. And out on the shore, I finally see what I want to write about: a small flock of stints that rises as one, turns, catches the sun, turns again ...

You've seen birds behaving this way, I'm sure. (Pigeons do it, too). Individually, they seem so ... well, individual. But flying together, they show a strange collective thinking and behaviour. If you watch such a flock, you begin thinking there's something uncanny going on. How do hundreds of individual movements translate into this graceful togetherness?

Flock-watchers had always thought that there must be a complex set of rules that each bird followed. Collectively, they produced the smooth, acrobatic and intricate movement we see. Complex movement? Must come from complex rules. So they thought.

Until 1986, when Craig Reynolds, a computer animator, blew a hole in that thinking. After many hours watching birds, he came to a quite different conclusion. Flock movement, he thought, could be explained by three very simple rules for each bird to follow:

• Move towards the average position of my flockmates; that is, towards where there are the most birds in the flock (cohesion).
  
• Maintain the same speed and direction of flight as my flockmates (alignment).
  
• Keep a discreet distance from my flockmates to avoid bumping into them. In fact, keep a discreet distance from all other objects (separation).

Reynolds wrote a programme to implement these rules, and used them to simulate the motion of a flock of birds on his screen. He called his simulated birds Boids.

Boids astonished everyone who saw them. Even in large numbers, they flew in a manner eerily reminiscent of their real-world counterparts. When the programme started, boids placed randomly all over the screen would quickly move towards each other and maintain the same direction. A stable configuration emerged at the centre of the flock; boids at the edges regulated their speeds to stay with the group. Even obstacles that Reynolds put in the boids' path did not trouble them. The simulated flock would approach a simulated pillar, split up at exactly the right moment, fly around it and reassemble -- just what birds would do.

As a whole, the simulated flock showed the same fluid, elegant moves that real ones did. In fact, they moved so realistically, so convincingly, across Reynolds' screen that ornithologists began to call him to find out what his rules were.

Reynolds had clearly hit upon something. But what was it? It was too early to say whether individual birds actually followed his rules -- but that hardly mattered, because flock behaviour was so spot on. This was the remarkable part, because nowhere in the Boids programme were there instructions about how the flock as a whole should behave. The rules applied only to individuals. Yet those rules were enough for the boids to "learn" how to form and maintain their flight pattern as a flock.

Collective behaviour, from three simple rules applied to individuals.

The boids experiment was successfully repeated with other animals. Programmes have simulated the behaviour of schools of fish and colonies of ants; even the movement of crowds entering a stadium, and this suggested where best to place ticket collectors. Reynolds' work even achieved some Hollywood fame: it was used in the stampede scene in "The Lion King".

All of which reinforced the same lesson. Simple individual rules produce complex collective behaviour. Complexity, from simplicity.

There are some interesting insights from these ideas. For example, the boids are an example of "bottom-up" programming. In more conventional "top-down" programming, you list thousands of individual instructions for your computer to follow. Bottom-up, you simply lay out a few broad guidelines from which the desired outcome emerges. Of course, there's hard work in finding those few guidelines. But if you can, your programme is simpler, easier to understand, and still does the job.

You might see our entire education system as top-down. We fill student minds with rigid stuff about one or the other subject, most of which they memorize. But we rarely teach them the ability to solve their own problems. So at the first metaphorical pillar in their paths, they fall flat instead of flowing smoothly around them like boids do. What if we instead gave our students a framework, some guidelines on how to learn? Hard work searching for those guidelines, yes. But we might then set them free to explore and learn on their own.

Another example: taken one at a time, our nerve cells simplicity itself. They react to chemical stimuli. Even more simply, they switch on, they switch off.

But when millions of such cells are connected in ways we don't yet fully comprehend, as in our bodies, something unexpected happens. Suddenly, you have thoughts, emotions, language, art, religion. In other words, intelligence, even though there's religion. And all from the ordinariness of nerve cells!

So now ask: did this article make sense? Whatever your answer, it is really just dots of colour sprayed on your screen according to some rules. Puts it in some perspective, you think?