2.2. Definitions of specific terms

Before going further, here is a short list of specific terms related to cellular automata that will be used in this chapter:


Figure 2. The cell as a finite-state machine connected to the cells in the neighborhood.


The most important features of the generic cellular automata computing model are: it is discrete in space and in time, it is finite and regular (except for the limit conditions), and it is parallel. The model can be regarded, in terms of computation theory, as an elementary single instruction multiple data (SIMD) architecture, since all cells perform identical operations [2]. The system is synchronous; therefore, in simulations, the algorithm that computes the next configuration can update cells' states in any order. The local rules, or functions, or laws, are deterministic, implying a global deterministic evolution (which is, however, often hard to

The complexity of the resulting structure, as a digital system, is depending on the number of cells' states, the number of cells (the dimension), and the dimension of the neighborhood,

Before going further, here is a short list of specific terms related to cellular automata that will

• cell—the elementary computing element, which is a finite-state machine (Figure 2),

• binary cellular automata—each cell has only two states, encoded on 1 bit,

• dimension of cellular automata—total number of cells,

Figure 2. The cell as a finite-state machine connected to the cells in the neighborhood.

predict).

related to the type of interconnection network [9].

168 From Natural to Artificial Intelligence - Algorithms and Applications

2.2. Definitions of specific terms

be used in this chapter:


A frequently used denomination of local rules was introduced by Wolfram in [8]. In the context of linear binary cellular automata with neighborhood dimension of three, each rule (which is a Boolean function with three variables) is designated by a decimal number, equal to the binary number obtained from the look-up table of the function. See Appendix 1 for most frequently used rules.

In applications, the synthesis of cellular automata implies to define the particular topology (number of states per cell, number of cells, type of interconnection network, dimension of neighborhood, border conditions), the local rules, timing conditions, and the seed, in order to obtain the desired functionality. For instance, in image processing applications, the initial configuration is the image. The local rules are established in order to obtain the desired function (for instance, edge detection). The automata will run for a certain number of states or until it reaches a stable configuration.

In the previous example, the input data are the initial configuration, the output data are the final configuration, and the computation related to the image processing task is done by the evolution of the global state, through local changes. Computation with cellular automata may also be considered in terms of propagation and combination of patterns, in an analogy with propagation of signals and logical combination of inputs.
