Conway's Life and generative music

Last summer, Brian Eno gave a talk in San Francisco on "Generative Music" that appeared as a transcript in In Motion Magazine.

I found his viewpoint interesting for several reasons. First, it's hard for me not to take notice when a celebrity expresses a view on a topic that interests me strongly, particularly when the topic is fairly esoteric. Second, when this happens, I'm usually bracing myself for some misunderstanding or far-fetched extrapolation on its universal significance. In this case I was pleasantly surprised. Eno may not be a mathematician, but he's played around with Life first hand. He's done some homework and knows its background reasonably well. Third, I'd like to see what an artist could do with Life after studying it at a deeper level--something that requires a little more insight than a multimedia exhibit with a random Life animation tacked on as homage to geek culture. Eno's comments give me some hope that this might happen one day.

Eno's remarks

The following remarks are from a talk by Brian Eno.

In the exploratorium the thing that absolutely hooked me in the same way as the Steve Reich piece had hooked me was a simple computer demonstration. It was the first thing I'd ever seen on a computer actually, of a game invented by an English mathematician called John Conway. The game was called Life. Modest title for a game.

Life is a very simple game, unlike the one we're in. It only actually has a few rules, which I will now tell you. You divide up an area into squares. You won't see the squares on the demonstration I'm about to do. And a square can either be dead or alive. There's a live square. Here's another one. There's another one. There's another one there.

The rules are very simple. In the next generation, the next click of the clock, the squares are going to change statuses in some way or another. The square which has one or zero neighbors is going to die, a live square that has one or zero neighbors is going to die. A square which has two neighbors is going to survive. A square with three neighbors is going to give birth, is going to come alive, if it isn't already alive. A square with four or more neighbors is going to die of over crowding.

These are terribly simple rules and you would think it probably couldn't produce anything very interesting. Conway spent apparently about a year finessing these simple rules. They started out much more complicated than that. He found that those were all the rules you needed to produce something that appeared life-like.

What I have over here, if you can now go to this Mac computer, please. I have a little group of live squares up there. When I hit go I hope they are going to start behaving according to those rules. There they go. I'm sure a lot of you have seen this before. What's interesting about this is that so much happens. The rules are very, very simple, but this little population here will reconfigure itself, form beautiful patterns, collapse, open up again, do all sorts of things. It will have little pieces that wander around, like this one over here. Little things that never stop blinking, like these ones. What is very interesting is that this is extremely sensitive to the conditions in which you started. If I had drawn it one dot different it would have had a totally different history. This is I think counter-intuitive. One's intuition doesn't lead you to believe that something like this would happen. Okay that's now settled (looking at screen), that will never change from that. It's settled to a fixed condition. I'll just show you another one. I'll show you this one in color because it looks nice. A little treat. (Laughter).

At the Exploratorium, I spent literally weeks playing with this thing. Which just goes to show how idle you can be if you're unemployed. I was so fascinated, I wanted to train my intuition to grasp this. I wanted this to become intuitive to me. I wanted to be able to understand this message that I'd found in the Steve Reich piece, in the Reilly piece, in my own work, and now in this. Very, very simple rules, clustering together, can produce very complex and actually rather beautiful results. I wanted to do that becuase I felt that this was the most important new idea of the time. Since then I have become more convinced of that, and actually I hope I can partly convince you of that tonight.

Life was the first thing I ever saw on a computer that interested me. Almost the last actually, as well. (laughter). For many, many years I didn't see anything else. I saw all sorts of work being done on computers, that I thought was basically a reiteration of things that had been better done in other ways. Or that were pointlessly elaborate. I didn't see many things that had this degree of class to them. A very simple beginnings and a very complex endings.


One should not assume that I share Eno's perspective entirely. In fact, he seems to be focused on the "natural" properties of Life. It's true that a surprising degree of structure emerges just from running the rules on different patterns. But people have been doing this for over 25 years now, and most of the early surprises have been observed, noted, and catalogued already. They're in little jars of virtual formaldehyde with carefully printed taxonomic names--or ought to be except it's admittedly the least exciting part of the enterprise. (Added 7-Dec-97: but see Mark Niemiec's web page for a giant step in this direction.)

My own interest lies in the very rare patterns, ones such as the space filler, or the stable reflector. These actually run counter to the intuition one develops from watching random patterns. They push the limits of what is possible. In principle, such patterns might emerge spontaneously, but not at any remotely human scale of time or space. A lot of these patterns can't be found just by running Life, but require an exhaustive search of a large combinatorial space. The result is something with an identifiable mathematical property, often (not always) combined with a visually appealing structure or symmetry.

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