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Skip to 0 minutes and 10 seconds In this lecture, you will learn about the particular type of computer models that we can use to study social self-organisation. These models are called cellular automata. You have already learned about agent-based models. Cellular automaton models can be seen as a particular class of agent-based models. In the following, we will discuss the basic principles of the cellular automaton model. The first important principle of a cellular automaton is its spatial structure. A typical example is a checkerboard structure, like the one you see here. Every cell in the structure is a location. And this location can be a position where an agent representing an individual is settled. We also call this a cellular world.

Skip to 1 minute and 9 seconds You can think of this as a very abstract and simplified model of how people live in the city. The cell represents the place of a house or an apartment. The household, or the individual living in the cell, has neighbours on each side.

Skip to 1 minute and 29 seconds Social self-organisation in the complex social system arises from the local interactions of individuals with each other. In the cellular automaton model, we can give a precise meaning to what we mean with this local interaction. Local interaction is the second important principle of a cellular automaton model. It means that individuals can only interact with others in the close distance around them. For example, in the abstract city on the checkerboard, you may only talk to the neighbours in the cells that have a common border with your cells.

Skip to 2 minutes and 11 seconds Here, you can see different types of neighbourhoods that are often used in cellular automaton modelling. In the leftmost picture you see a so-called von Neumann neighbourhood. The cell in the centre has four neighbours– one to the north, one to the south, one to the west, and one to the east of its own position. In the next picture, you see a so-called Moore neighbourhood. Here you have eight neighbours. So also the neighbours on the corners bordering to yourself are your neighbours. And we can make this neighbourhood bigger, like in the five-by-five Moore neighbourhood that you see in the rightmost picture.

Skip to 2 minutes and 56 seconds This difference between these neighbourhoods can be seen as a model of how local the interaction is. In the leftmost von Neumann neighbourhood, you have the most local interaction. You interact only with a few neighbours. In the rightmost, you have quite many neighbours. And, of course, we can build in a lot of variation in how exactly we will model these neighbourhoods. You can think of the example of the spreading of a rumour. In the von Neumann neighbourhood, people would only talk to their nearest neighbours. In such a world, a rumor would spread only very slowly. But in a Moore neighbourhood, you have more neighbours to talk to. You have more neighbours from whom you can hear the rumour.

Skip to 3 minutes and 41 seconds And it will spread faster, because it can come from people who are more steps away from you. Of course, there can be many other ways to model neighbourhoods. Like the example that you see here. And as you see in this example, the red neighbourhood is more local than the yellow. So in general, the way you model the neighbourhood can be used to express how local or global the interaction model is. This can be used to model the effects of conditions like communication technology or geographic density of a population on the outcomes of social self-organisation. So far, we have seen two important principles– the spatial structure and local interaction.

Skip to 4 minutes and 29 seconds But how can we model what happens in interaction in a cellular automaton? For this there are again two basic principles. The first principle is that agents in the cells have a state. The state represents, for example, their opinion or their ethnicity. Typically, a state is modelled as a number. So for example, an agent may have the states one, two, or three, representing which out of three possible political parties the agent would vote for. The second important principle is that states can change. Agents can change their states. How they change their states depends on both their own state and states of the neighbours.

Skip to 5 minutes and 16 seconds So, for example, if the majority of your neighbours believe a certain rumour, you might also start to believe it. But when can the state change occur? There are different ways to model this. Time is discrete in cellular automaton models. That is, time moves on in steps, or rounds. In some models, all agents change their states in every round at the same time. They take their own state and that of their neighbours from the previous time point, and then all change to a new state. In other models, one agent at a time can change the state, depending on the current situation. Typically, agents are then selected at random for a state change.

Skip to 6 minutes and 2 seconds Moreover, we distinguish two important types of state change dynamics. The first one can be called influence dynamics, and the second one migration dynamics. In influence dynamics, agents do not change their location. But they change their state. For example, you may change your opinion from pro something to con something, because the majority of your neighbours is also against it, has a con opinion. In migration dynamics, the state that the agent changes is actually the location. That is, an agent may move to another place in the world depending on the current state of the neighbourhood. In the lecture on agent-based models, you have already encountered a well-known example of a migration dynamic– Schelling’s model of ethnic segregation.

Skip to 6 minutes and 57 seconds We have now seen the three most important principles of a cellular automaton model. To summarise, there’s a spatial structure, like on a checkerboard. Second, interaction is local. Agents in the cell only interact with cells in a close neighbourhood around them. Third, interaction is modelled as a state change. Agents have states that they can change. And whether and how they change it depends on the states of the other agents in their neighbourhood. State change can be both change of an agent characteristic or change of the location of an agent.

Skip to 7 minutes and 41 seconds In the remainder of this lecture, we will look into a simple example of a cellular automaton model. This is a model for the formation of opinion clusters. We will do this in the next movie.

What is cellular automata modelling?

This video introduces cellular automata modelling as a special class of agent based models. We can use these models to get a better understanding of self-organisation.

But what exactly can you model with this and how does it work? What are the basic principles of Cellular Automata and how do agents interact? What can we explain using these kind of models?

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Decision Making in a Complex and Uncertain World

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