15 days I wrote the blog “yet another blog about the “Conway’s Game of Life” . My purpose was convincing you that very simple individual rules could produce group patterns. This patterns emerge from the individuals interacting with their environment and nothing else.
I promised I was letting the best for today. So here it is. You probable were wondering how complex this group patterns could get with the right positioning. Actually what I showed in the previous blog were just the most basic and well known examples. There are much more complex things. Take a look at the next youtube video, but start it at minute 1:10, since you don’t need explanations about the game of life anymore.
That is very cool but there is more. Some very simple patterns can produce very unstable sequences (chaotic) structures. You can go here and click on run. It takes 5206 to converge (Here is a list of other long-lived patterns that you may want to try). Of course you can also randomize the canvas and wait. It could easily happen that you stare at your screen for a few days, weeks. What to say? The universe is still here in a constant accumulation of simple interaction of small particles. Even in a simple game like this would be almost (just giving a benefit of doubt) impossible to predict the final stage, and we are starting just five individuals.
You may say, simply run the game and then you have your prediction. First, is that really a prediction? Second, there is a practical problem if you want to apply that to, say, the universe. You need another one to simulate it (and a faster one so you can use the prediction). There is another solution. Simplify the individuals. Instead of simulating a whole human being, just grab the main characteristic of his behaviour and you may learn something of the factors you picked it up. This is the theoretical background of my thesis and I will be talking about this in many different ways.
But let’s go back to the “Conway’s Game of Life” to stress two important things:
- Actually the “Conway’s Game of Life” is a more complicated version of something even more simple that produce complex patterns. It is just another example of a Cellular Automata. Don’t worry, my next blog is going to be about it. For now, I am just going to add that the “Conway’s Game of Life” is a 2 dimensional games. The simplest cellular automata has just 1 dimension, and still produces chaos
- The “Conway’s Game of Life” has the same computational power as a universal Turing machine. I don’t know if I will be talking about the Turing machine at some but, for now, just consider that this game is “as powerful as any computer with unlimited memory and no time constraints: it is Turing complete”.
Three important conclusions so far:
- The initial conditions (patterns) determine dramatically the ending result.
- Chaos could come me from very simple conditions. That is to say, you don’t need complicated models to get interesting environments. You are going to find head aching problems even in the restrictive and conditioned environment of math.
- The predictability inside chaos is still possible. You just need another universe :D. Here, I am very satisfied and assert that chaos is different randomness. You cannot predict the latest. The question, still open in the science, is “does randomness exist at all?”
Next entry: Cellular Automata