Information Transfer by Particles in Cellular Automata
Particles, gliders and domain walls have long been thought to be the information transfer entities in cellular automata. In this paper we present local transfer entropy, which quantifies the information transfer on a local scale at each space-time point i
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CSIRO Information and Communications Technology Centre, Locked Bag 17, North Ryde, NSW 1670, Australia School of Information Technologies, The University of Sydney, NSW 2006, Australia [email protected] Abstract. Particles, gliders and domain walls have long been thought to be the information transfer entities in cellular automata. In this paper we present local transfer entropy, which quantifies the information transfer on a local scale at each space-time point in cellular automata. Local transfer entropy demonstrates quantitatively that particles, gliders and domain walls are the dominant information transfer entities, thereby supporting this important conjecture about the nature of information transfer in cellular automata.
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Introduction
Design and analysis of complex nonlinear behavior in artificial life systems has recently begun to consider the concept of information transfer (e.g. via influence of agents over their environments [1], in co-ordination between individual modules of modular robots [2], and inducing neural structure in robots [3]). Nowhere is the consideration of information transfer more clear than in studies of cellular automata (CAs), where the emergent structures known as particles, gliders and domain walls have long been suggested to be the information transfer entities therein [4,5]. Importantly, information transfer is also viewed as an important component of complex behavior beyond the field of artificial life (e.g. self-organization caused by dipole-dipole interactions in microtubules [6]). Despite the abundance of complexity measures though (e.g. [7,8]), quantitative studies of information transfer in complex systems are noticeably absent. We derive a measure of local information transfer from the transfer entropy [9], an existing averaged information-theoretical measure. Local transfer entropy characterizes the information transfer into each spatiotemporal point in a given system rather than providing a global average over all points in an information channel. Local transfer entropy facilitates close study of parameters of the average transfer entropy, and is independently useful in highlighting or filtering “hot-spots” in information channels. We apply local transfer entropy to Elementary Cellular Automata (ECAs), a class of simple yet powerful discrete dynamical models. Local transfer entropy profiles for ECAs highlight the particles, gliders and domain walls as the dominant information transfer entities, importantly providing the first quantitative evidence for this widely-accepted conjecture about the nature of information transfer in CAs. M. Randall, H.A. Abbass, and J. Wiles (Eds.): ACAL 2007, LNAI 4828, pp. 49–60, 2007. c Springer-Verlag Berlin Heidelberg 2007
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J.T. Lizier, M. Prokopenko, and A.Y. Zomaya
Information Transfer in Cellular Automata
We begin by introducing cellular automata (CAs), a renown example of complex systems, and discuss the importance of information transfer therein so as to contextualize our motivation. CAs are discrete dynamical systems co
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