You may be asking at this point, "What, exactly, is interesting about the game of Life from the perspective of complex systems science?" Well, to my mind, the game of Life and other cellular automata are perhaps the simplest idealized models of complex systems, and they illustrate many of the qualities of the real-world complex systems that we're interested in. For example, in the game of Life, we have the ingredients of real-world complex systems that I listed in the first unit. We have large numbers of simple components, that is, the cells; obeying relatively simple rules, we saw the rules of the game of Life; they have limited communication -- each cell only directly communicates with its nearest neighbors; and there's no central control. We also see, in an idealized way, the outcomes of complex systems that we find the most interesting, namely complicated dynamics, emergent self-organizing behavior, meaning that the collective outcome of the components, following their simple rules, can produce interesting, hard-to-predict yet organized behavior. For example, if we set up from a random initial configuration which has high entropy, in the sense of a random box of gas, and let the system run, we see a complicated transition to rather organized structures, these fixed points, or periodic structures, these "blinkers," and so on, that have low entropy configurations with interesting regularities. So there's a connection here between the game of Life or cellular automata and information theory. Via the rules, the entropy of initial configuration is reduced. We'll also see that in the game of Life and many other cellular automata, we can use these structures to produce sophisticated information processing. We'll also show how evolution, via genetic algorithms, can shape their information processing abilities to be useful for the survival of the system. One other aspect of interest that we haven't seen yet is that John Conway designed Life to be open-ended, in the sense that its behavior wouldn't be limited to a finite set of configurations. In this model, minilife.nlogo, we have a finite grid that wraps around the edges. This finite configuration actually limits the potential of what we can see in the game of Life. One of our teaching assistants, Max Orhi, has developed a fantastic, open-ended simulation of Life called gameoflife.nlogo, which you can also download from our course materials site. Let me open it now. This is the interface for this more complicated simulation. And it is somewhat complicated. But let me just give you a little tour of it, and then you can play with it on your own. This version of the game of Life lets us do several things we couldn't do in the mini-Life version. First, it lets us insert patterns, specific patterns; if we go to Patterns, here, these are different patterns that people in the game of Life community have discovered as being quite interesting, and we can insert these. So I'm going to -- right now we can insert a glider. To do that, we click on Edit, and then just click here, and there's a glider. And then I can go for one iteration ... again, or I can just go. And what's interesting here is that now we don't have a finite configuration anymore. Here, in this "map of the universe," we see where this world over here ends, right down here, and the glider has gone off into space, to be forever lost in space. It doesn't wrap around. All right, so let's stop that. Let's set up again to clear everything. Now, let's just, let's do the same thing, but now, let's put in lots of different gliders to see what happens. Now, if we go, they all fly off and we can see them kind of flocking to, to go off into space forever. It's open-ended, in that sense. Okay, let's set up again and look at one other structure -- a glider gun. This is a fairly complicated structure. This was invented by somebody playing around with the game of Life, and what this structure does, just obeying those same rules, is the following. I'm going to slow it down a little bit, and go. What this does is it kind of acts as a machine to produce gliders. And you can see that the gliders go off in this direction. You can see the stream of them going off this way in the map of the universe. And you can see the workings of the machine here, that are building these gliders, in some sense. So this is a very open-ended kind of process, where you can just build an infinite number of gliders to have them go off into infinity here. Okay, so that's another structure. It turns out that the glider gun and the gliders are very important when we go to try and perform information processing tasks using the game of Life. We'll talk about that a little bit later. There's a lot of other patterns you can play with, and a lot of features that you can read about in the Info tab, and we'll have some exercises on the homework dealing with this model, as well as mini-Life.