What are the mechanisms underlying biological systems’ ability to transform themselves: the ability of structures to replicate for their own goals, or to meet the specific goals of the system or environment to which they belong? What kind of evolutionary process underlies the emergence of the simple structures which joined together and replicated to produce the life on earth? How can we reproduce these functions in digital machines? More generally, what are the common elements shared by complex physical, biological, social and artificial systems?
TopIntroduction
What are the mechanisms underlying biological systems’ ability to transform themselves: the ability of structures to replicate for their own goals, or to meet the specific goals of the system or environment to which they belong? What kind of evolutionary process underlies the emergence of the simple structures which joined together and replicated to produce the life on earth? How can we reproduce these functions in digital machines? More generally, what are the common elements shared by complex physical, biological, social and artificial systems?
In this chapter, we will examine the fundamental problem of how we can use 1 and 2-D Cellular Automata to model biological phenomena. Modeling is today a fundamental method in many sciences, ranging from the neurosciences and nanotechnology to genetic engineering (for a review see Freitas, 2004).
As we saw in Chapter 2, 1-D Cellular Automata consist of a large number of elementary units. Interactions among the units are determined by a single, deterministic, local rule that gives rise to forms of self-organization and a wide range of emergent shapes. Inside the automaton, we distinguish particles which self-organize and propagate through time and space. These are so-called gliders. The dynamics of these emergent structures can lead to the extinction of other particles, the generation of new chaotic or periodic structures (new gliders) and sudden transitions from an ordered to a chaotic state.
Whether we start from Wolfram’s qualitative classifications (Wolfram, 1984), Crutchfield’s analytical computational mechanics (Crutchfield & Young, 1989; Crutchfield, 1994; Hanson & Crutchfield, 1997) or Wuensche’s systematic analysis of overall dynamics (Wuensche & Lesser, 1992), we are limited to CAs with a small number of cells. However, there exist alternative methods that allow us to consider systems with large numbers of cells and multistate CAs (Bilotta et al., 2003a). In our own work, we have used Genetic Algorithms to identify complex rules for 1-D multistate automata, applied new techniques to analyze the emergent, spatio-temporal patterns they produce, developed computational methods to identify these patterns automatically, and studied the way in which local or deterministic rules are translated into genetic structures. As reported in several chapters of this book, we have used quantitative and qualitative analysis to identify the organizational laws underlying emergent structures, focusing on a small set of production rules shared by all these systems (Bilotta & Pantano, 2001). We also adopted an alternative way of modeling 1-D CAs, using the Universal Neuron approach first proposed by Chua and co-workers (Chua 2006; 2007; 2009). This method allows us to identify similarities in the behavior of different systems and to identify associations between the characteristics of the automaton and the dynamic system to which it gives rise. The models we have created make it possible to generalize from elementary CAs (ECAs) to multistate systems. The results show how universal neurons can generate rules with emergent properties (Bilotta & Pantano, 2008).