The outcomes as you already know can be quite surprising as you can see here. The good thing is that why they can't be quite surprising, there are different kinds, different classes of outcomes of queries and there are only four class of piggy back here on a very influential book, A New Kind of Science from Stephen Wolfram and these are these four classes basically of all kind of models. It's a little bit pseudo four class because there are many more because the fourth class is a little big but let's start like that. One class we've already seen of the possible outcomes of any kind of model especially an agent-based computer simulation and that's a homogeneous state or an equilibrium. So you've seen that in Schelling for example. So that means the model evolves into a stable homogeneous state and any randomness of the initial pattern actually disappear. So in Shelling's model, we went to this state of this level of segregation and that's when it stopped. You can run many times and that's where you can make your invariant distribution your stationary distribution. Out of this, the accumulation of these different equilibrium states which always might be a little bit different but at the end, it stops and it gives you a clear data points. Segregation is 85.6 percent for example. Now, another possible outcome is a cycle or periodic orbits. So the model evolves quickly into a stable or oscillating structure. Some randomness may still remain but there is a clear cycle with data, what is called a periodic orbits. For example you have day and night and day and night, that's a periodic orbit, or you can have three different stated, oscillates among these three different states or you have a winter, spring, summer, fall or in the economy, some kind of cycle goes up and down. You can see these cycles and it's not like it stops at one point, but you can make a prediction about these cycles and there are special methods you can use to analyze this kind of periodic behavior. That's also a possible outcome and you can have. Another outcome is randomness or apparent randomness, chaotic behavior. So you can start with a completely deterministic process, the process is very well-defined. It is defined but you lose too much information on the way and you cannot track for example the initial conditions and if it's sensitive to this initial conditions, the initial conditions that it started with, you cannot make any predictions anymore. You lost all the information on the way and these are called chaotic systems. But at the end also for all practical purposes are apparently random. So the model evolves in a random or pseudo-random because actually they're still determined. But for you as the observer, they're random or chaotic manner. Any stable structure are quickly destroyed by interactions with the surrounding noise and lack of information. Now, honestly if something is really truly random, you cannot really make predictions, especially predictions that are often useful because if they are two different events and they're uniformly, you can still make predictions on the level of the level of the random distribution and you can say, well, there's a 50-50 chance but you cannot predict anything beyond that. You can say there's a 90 percent 10 percent chance but beyond that, it's random. So the level of science then gets restricted to this higher level of distributions. Last but not least, and that's why I said it's like a pseudo four categories because the last category is extremely big and this is complex. Same as there, the non-linear is like the sociology of non-elephants, the complex is like an aggregate term but there are many different things thrown into that. We do not understand yet. Computational methods helps us to dig a little bit deeper into that and try to piece it apart maybe make a taxonomy of these different complex pattern. But basically, the modeling evolves by forming local structures that interacts and act in complex ways and are able to survive for a long time. So you also might be at the end part of a periodic orbit for example but it might be that a cycle takes around 8,000 years. So nobody ever observed one because we didn't document history before 8,000 years and it might be in some cultures are more than the cyclical worldview, it might be that history returns itself, we just wouldn't know at this point. For us, it seems like there seems to be something that's going on and we can still make some predictions. But for now, we don't know. So it might be that it's part of something different just to say like one aspect of it and they can survive for long period of times. Also these local structures that help you to make predictions, but then again, you might lose them. So they're not random but not also clearly determined, they're somewhat predictable.
