Life at the Edge of Chaos

Emergent behavior occurs in many systems. For catalysis in porous systems bond or site percolation is an important example. It describes the probability that in a statistical network a particle can move through the system. It models the mass transport through a porous medium. This is illustrated in Fig. where a two-dimensional network is 

Wolframl discovered analogous behavior from simulation studies with cellular automata. His work shows that, notwithstanding well-defined short-range interaction rules between components on a microscopic level, macroscopic dynamic behavior can become unpredictable. This implies that external disturbances can have an important outcome on both temporal and structural events. This is consistent with a condition of life, where there is change due to evolutionary response. Examples of the four basic classes of behavior Wolfram discovered are shown in Fig. 9.11. 

In Wolfram s computational work pattern formation is studied on a two-dimensional lattice. Interaction rules are defined between lattice squares for the evolution of blackness 

Hence rules have been set up in which the color of the cell in a row n depends on the coloring of the three neighboring cells in row n — 1. Each system is determined by eight different rules. In total, 256 different choises can be made, generating an amazing variety in pattern behavior. Wolfram distinguishes four classes of behavior. 

Following the ideas of AndersonP l, Langton , who is one of the founders of artificial life research, coined the phrase life at the edge of chaos . To identify the condition of life for a cellular automaton system, he defined a control parameter A. For a cellular automaton with K states and N neighbors the A parameter is defined as follows. An arbitrary state Sq is chosen as a quiescent state, as for instance, the solution zero, with for the logistic map. If there are n, transitions defined to state Sq, the remaining 

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Iewin92] Lewin, R., Complexity Life at the Edge of Chaos, Macmillan Publishing Company (1992). 

Lewin, R. (1993). Complexity. Life at the Edge of Chaos , p. 177. Macmillan, New York. Lyman, W. (1982). Handbook of Chemical Property Estimation. Academic Press, New... 

The evolutionary field a) R. Lewin, Complexity - Life at the Edge of Chaos, Macmillan, New York 1992 Die Komplexitdtstheorie, Hoffmann Campe, Hamburg 1993 b) F. Cramer Chaos and Order, VCH, Weinheim 1993 Der Zeit-baum, Insel, Franfurt a. M. 1993 Symphonie des Lebendigen, Insel, Frankfurt a.M. 1996. 

C. G. Langton, Life at the Edge of Chaos, in C.G. Langton, C.Taylor, J.D. Farmer, S. Rasmussen (eds.) Artificial Life II, Addison-Wesley, Redwood City, p. 41 (1992)... 

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