Geosimulation - Cellular Automata
Department of Geography
Eberhard-Karls-University of Tübingen
Abstract. The following paper will cover an overall view of cellular automata. Due to the fact that the method will be considered from the outset, it is accessible not only for specialists. Further I tried to broach the history of cellular automata and the first well-known application “Game of Life”. Moreover a practical application will illustrate the potential of cellular automata on the basis of a NetLogo forest fire model. In addition to a short analysis of this geosimulation, a continuative and deeper going paper will be mentioned. After this example, interested readers should be able to appraise the value of cellular automata’s implementation. Finally, the work will be rounded off with the mention of the most significant disadvantages and problems.
1 Introduction – Why do we use Geosimulation at All?
In order to construct a useful model of reality, at first, it is necessary to focus on the essential aspects of the general problem. Based on that, it is possible to analyze the specific situation. Moreover – and that is the biggest benefit – we will be able to simulate several scenarios and predict their outcome without conducting experiments. Generally spoken a simulation helps to simplifiy and deal with complex relations of life in a cheaper, less dangerous and time-saving way.
The application of cellular automata as a geosimulation also postulates the extraction of important rules. So the first barrier of using cellular automata seems to be one of the biggest (Openshaw 2000, p. 244), therefor we can pattern for example the evolution of life.
At the end of this paper I will discuss some other disadvantages and problems with the application of cellular automata. Prior to this I will discuss the function as well as the potential of cellular automata in detail. Prior to the conclusion one example of use will complete the paper.
2 Cellular Automata as a Method Not Only for Natural Sciences
As Fredkin said “Living things may be soft and squishy but the basis of life is clearly digital.” (Openshaw 2000, p. 241), everything follows a consequential path. Let us have a look at a snowflake: Each format has its own constructial drawing but everyone is absolutely symmetrical. How do the individual frozen molecules know where they have to fix to be part of this form? There is of course no “constructer” arranging the smallest parts of the snowflakes. Natural sciences tell us that it is founded in intermolecular relationship, so a snowflake is just a macroscopic projection of its microscopic structure. The structure of crystals for example is the outcome of the same phenomenon (Beckmann 2003, S.2).
As we can easily imagine, the method of cellular automata has a lot of applications in physics, chemistry and biology. Scientists in these subjects gladly apply cellular automata because issues follow more deterministic models than in social sciences. In the following chapters I will try to illustrate to what extent the cellular automata could also be used in other subjects, especially in geographical matters. Human geography is often concerned with topics originating sociology, economy, urban development, crisis management and other issues which cannot only be explained by numbers and formulas. Nevertheless the method of cellular automata can be useful to understand some important issues (cf. Atkinson 2000, p. 73).
3 A Historical Background of Cellular Automata
To complete the introducing chapters it is helpful to show the first steps of the technique. The idea to simulate the behavior of animate beings is as old as the invention of computer itself (Openshaw 2000, p. 236). In 1966 John von Neumann and Stanley Ulam had their breakthrough as they implemented a self-contained replication of individual cells (Openshaw 2000, p. 241; Pohlmann 2007, p. 2). Naturally, cells were not able to decide themselves if they will increase their population or not. Instead, the development of their population depends heavily on their neighborhood as can be seen in chapter 4.2.
In 1970 John Hortin Convay invented the well-known “Game of Life” which should simulate the evolution of a population of cells on a schematic grid (Rommenay 2006, p.11). This fundamental example of the cellular automata will be deepened in chapter 5.
4 The Operation of Cellular Automata
As aforesaid we will now focus on how the cellular automata actually work. All explanation is based primarily on the diploma thesis by Dirk Rommeney (2006) but can also be found for example in the paper of Beckmann (2003).
4.1 The Cell
Each cell is called a cellular automaton, where the development of the model arises from. These cells can be arranged in different two-dimensional grids as shown in figure 1.
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Figure 1: Different types of grid: (a) rectangular, (b) alveolar and (c) triangular grid. Source: Rommeney 2006, p. 5
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Figure 2: A Torus with bonded edges. Source: ROMMENEY 2006, p. 6"
Mostly we use a rectangular grid because it is more accessible. A one or three dimensional diagram is possible as well, though it is easier to calculate on a two dimensional grid while providing a sufficient degree of realism. In general it is problematic to visualize temporal progress in three-dimensional spatiality (Rommeney 2006, pp. 5).
In the following I will consider only two dimensional rectangular grids. This grid must have a defined space to program it. Implementations of such grids usually transform the 2d surface into a torus in order to avoid (falsification at the) edges (Rommeney 2006, p. 6). So the calculation of the cellular automata is based on the torus while it is presented as a two-dimensional grid.