3. Theoretical and practical issues

2.3. Taxonomy of cellular automata

170 From Natural to Artificial Intelligence - Algorithms and Applications

(function and/or phenomenology).

corners (Figure 3).

sional cellular automata [11].

The classification of cellular automata is based either on structure (topology) or behavior

The topology refers mainly to the type of network and local connections (neighborhoods and boundary conditions). In linear cellular automata, the cells are connected in a row (vector) to their nearest neighbors. Further subdivision of linear cellular automata is based on the neighborhood dimension, which is one of the main factors that affect the complexity of the cell. In two-dimensional cellular automata models, the interconnection network is two dimensional, typically rectangular, but also hexagonal networks have been explored for specific applications. However, topologically any two-dimensional network can be transformed in a rectangular one, by choosing an appropriate neighborhood [5]. In typical rectangular connections, there are two most used neighborhoods: von Neumann neighborhood which contains the four adjacent cells on the vertical and horizontal lines, and the central cell itself; and Moore neighborhood that contains the lateral neighbors, the central cell, and the cells adjacent at

The theoretical analysis of two-dimensional cellular automata is an open field of research, and most often, the results are extensions of the better-known case of linear automata. Twodimensional cellular automata are very important in applications, as for instance in image processing, where the image corresponds directly to the configuration of the system. Most of modeling applications also involve two-dimensional extensions, therefore, use two-dimen-

Probably the most important contribution in understanding cellular automata capabilities as a computer model is Wolfram's experimental approach [8]. Wolfram explored the behavior of linear cellular automata for all rules (with a neighborhood of dimension 3), starting from different "seeds" or initial states. Wolfram established a classification based on the statistical

Figure 3. Neighborhoods in two-dimensional cellular automata: von Neumann (left) and Moore (right) neighborhoods.

2.4. Phenomenology of cellular automata—Wolfram's taxonomy

This section discusses specific issues of cellular automata that one should be aware before deciding to use or investigate this model.
