Are complex systems hard to evolve?

Abstract

Evolutionary complexity is measured here by the number of trials/evaluations needed for evolving a logical gate in a nonlinear medium. Behavioral complexity of the gates evolved is characterized in terms of cellular automata behavior. We speculate that hierarchies of behavioral and evolutionary complexities are isomorphic up to some degree, subject to substrate specificity of evolution, and the spectrum of evolution parameters.2009 Wiley Periodicals, Inc. Complexity 14: 15-20, 2009 Key Words: logic gates; evolution; cellular automata; complexity T here are many ways to measure the complexity of a system [1-3]. For example, having a problem we can estimate its complexity as the number of steps a computer takes to solve the problem (computational complexity). A descriptive complexity of a system is evaluated by the length of a minimal program/ model representing the system. Complexity of a finite state machine can be classified in sets of regular languages accepted by the machine. There are also measures based on how difficult it is to predict the evolution of a system.There are, however, few-if any-results related to the comparison of different measures of complexity. This short article aims to raise readers' awareness of the subject and to invite them to undertake research in ''comparative complexity.'' We compare the evolutionary complexity of logical functions (time required to evolve the functions) with the behavioral complexity of the functions (complexity of sequences of data iteratively processed by the functions).Nonlinear spatial extended media-liquid crystal [4] and Belousov-Zhabotinsky system [5]-were chosen as substrates of various logical gates' evolution because these media are possibly the best prototypes of nonclassical, unconventional, computing devices [6]. One-dimensional cellular automata were then selected as substrates to implement the gates evolved because the automata are good approximators of the real world [7], the space-time dynamic of the automata is easy to visualize, and methods for exploring complexity of the automata are well-established [8][9][10][11][12]. EVOLUTIONARY COMPLEXITY OF BOOLEAN GATESWe infer hierarchies of evolutionary complexity from computational and experimental laboratory studies of evolving of logic gates in liquid crystal [4] and excitable chemical medium [5]. See full details in the article cited, here we provide only a very brief overview of the results.

Discovering Boolean Gates in Slime Mould

“…• Gates in cellular automata [37]: OR NOR AND NAND XOR • Gates in Physarum: AND OR NAND NOR XOR XNOR We see that in all systems quoted the gate XOR is the most difficult to find, develop or evolve. Why is it so?…”

Designing Complex Dynamics in Cellular Automata With Memory

“…In the latter case, s Figure 11 illustrates three different kinds of dynamics emerging in ECAM rule 126, for some values of τ . 5 Exploring different values of τ , we found that large odd values of τ tend to define macrocells-like patterns [Wolfram, 1994], [McIntosh, 2009], while even values are responsible for a mixture of periodic and chaotic dynamics. Figure 11(a)i illustrates large periodic regions with few complex patterns traveling isolation developed by function φ R126min:3 .…”

“…Complexity of a system is almost never quantified but often related to unpredictability. Theory of cellular automata (CA) refers to complexity its entire life [von Neumann, 1966], [Adamatzky & Bull, 2009], [Boccara, 2004], [Chopard & Droz, 1998], [Hoekstra et al, 2010], [Kauffman, 1993], [Margenstern, 2007], [McIntosh, 2009], [Mainzer & Chua, 2012], [Mitchell, 2002], [Morita, 1998], [Margolus et al, 1986], [Poundstone, 1985], [Park et al, 1986], [Toffoli & Margolus, 1987], [Schiff, 2008], [Sipper, 1997], [Wolfram, 1986], [Martínez et al, 2013a], [Martínez et al, 2013b]. Due to transparency of cellular automata structures their complexity can be measured and analysed [Wolfram, 1984a], [Culik II & Yu, 1988].…”

On the Dynamics of Cellular Automata with Memory

“…In the latter case, s of τ . 2 Exploring different values of τ , we found that large odd values of τ tend to define macrocellslike patterns [40,26], while even values are responsible for a mixture of periodic and chaotic dynamics. Figure 4(a) illustrates large periodic regions with few complex patterns travelling isolation developed by function φ R126min:3 .…”

“…Complexity of a system is almost never quantified but often related to unpredictability. Theory of cellular automata (CA) deal with complexity its entire life [34,2,11,12,14,26,28,39,22]. Due to the transparency of CA structures, their complexity can be measured and analyzed [38,13].…”