A New Kind of Science

Wolfram, Stephen; Gad‐el‐Hak, Mohamed

doi:10.1115/1.1553433

Cited by 1,439 publications

(1,990 citation statements)

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“…Finally, the most interesting class 4 contains all remaining automata which, according to Wolfram, display behaviors "more complex than chaos" being possibly capable of universal computation. The famous Game of Life is a CA of class 4 [5].Wolfram has recently evoked class 4 automata as paradigms for the emergence of life [2]. Our findings support this picture in the sense that specific initial conditions in confined systems yield highly non-trivial spatio-temporal periodic patterns while the overall picture is dominated by long transients.…”

supporting

confidence: 78%

Spontaneous emergence of spatio-temporal order in class 4 automata

Gallas¹,

Herrmann²

2005

Physica A: Statistical Mechanics and its Applications

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We report surprisingly regular behaviors observed for a class 4 cellular automaton, the totalistic rule 20: starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in space. This is the first evidence that different types of spatio-temporal order can emerge under specific conditions out of disorder in the same discrete rule based algorithm.Cellular automata (CA) are discrete dynamical systems of many degrees of freedom that have been used successfully to describe a plethora of nonlinear phenomena ranging from pattern formation to chaos, have been applied for modelization in biology, geology, chemistry, sociology, etc and have even been proposed as minimal computer. In a seminal and remarkably influential work Wolfram [1,2] distinguished four classes of behavior for binary CA, i.e. those with a local degree of freedom σ i which is either σ i = 1 or σ i = 0. In class 1 all initial configurations evolve to a fixed point, when all cells are either one or zero. Automata of class 2 evolve to spatially static structures with eventually short-lived temporal oscillations. Class 3 automata produce selfsimilar patterns that can be characterized as discrete chaos. Finally, the most interesting class 4 contains all remaining automata which, according to Wolfram, display behaviors "more complex than chaos" being possibly capable of universal computation. The famous Game of Life is a CA of class 4 [5].Wolfram has recently evoked class 4 automata as paradigms for the emergence of life [2]. Our findings support this picture in the sense that specific initial conditions in confined systems yield highly non-trivial spatio-temporal periodic patterns while the overall picture is dominated by long transients. In

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supporting

confidence: 78%

Spontaneous emergence of spatio-temporal order in class 4 automata

Gallas¹,

Herrmann²

2005

Physica A: Statistical Mechanics and its Applications

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“…it evolved in a world that is itself computational. Computationalistic ideas have been defended by a variety of authors like Wolfram [31], Schmidhuber, Lloyd [21], Floridi and Zuse: "The entire universe is being computed on a computer, possibly a cellular automaton." 2 It is clear that this form of computationalism is a purely metaphysical position which can not be verified at best, but which prima facie is at variance with plain observations we can make in everyday life: e.g.…”

Section: A Thermodynamic Interpretation Of Solomonoff's Programmentioning

confidence: 99%

Between Order and Chaos: The Quest for Meaningful Information

Adriaans

2009

Theory Comput Syst

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The notion of meaningful information seems to be associated with the sweet spot between order and chaos. This form of meaningfulness of information, which is primarily what science is interested in, is not captured by both Shannon information and Kolmogorov complexity. In this paper I develop a theoretical framework that can be seen as a first approximation to a study of meaningful information. In this context I introduce the notion of facticity of a data set. I discuss the relation between thermodynamics and algorithmic complexity theory in the context of this problem. I prove that, under adequate measurement conditions, the free energy of a system in the world is associated with the randomness deficiency of a data set with observations about this system. These insights suggest an explanation of the efficiency of human intelligence in terms of helpful distributions. Finally I give a critical discussion of Schmidhuber's views specifically his notion of low complexity art, I defend the view that artists optimize facticity instead.

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“…This technique has been used with great success in the field of cellular automata e.g. [16]. For 1D cellular automata the spatio-temporal aspect can be captured by a 2D image of the evolution of the single line of cells.…”

Section: Film Analysis Vs Quantitative Studiesmentioning

confidence: 99%

Self-adaptation and Dynamic Environment Experiments with Evolvable Virtual Machines

Nowostawski

Epiney

Purvis

2006

Engineering Self-Organising Systems

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The Department of Information Science is one of six departments that make up the School of Business at the University of Otago. The department offers courses of study leading to a major in Information Science within the BCom, BA and BSc degrees. In addition to undergraduate teaching, the department is also strongly involved in postgraduate research programmes leading to MCom, MA, MSc and PhD degrees. Research projects in spatial information processing, connectionist-based information systems, software engineering and software development, information engineering and database, software metrics, distributed information systems, multimedia information systems and information systems security are particularly well supported.The views expressed in this paper are not necessarily those of the department as a whole. The accuracy of the information presented in this paper is the sole responsibility of the authors. CopyrightCopyright remains with the authors. Permission to copy for research or teaching purposes is granted on the condition that the authors and the Series are given due acknowledgment. Reproduction in any form for purposes other than research or teaching is forbidden unless prior written permission has been obtained from the authors. CorrespondenceThis paper represents work to date and may not necessarily form the basis for the authors' final conclusions relating to this topic. It is likely, however, that the paper will appear in some form in a journal or in conference proceedings in the near future. The authors would be pleased to receive correspondence in connection with any of the issues raised in this paper, or for subsequent publication details. Please write directly to the authors at the address provided below. (Details of final journal/conference publication venues for these papers are also provided on the Department's publications web pages: http://www.otago.ac.nz/informationscience/pubs/). Any other correspondence concerning the Series should be sent to the DPS Coordinator. Abstract. Increasing complexity of software applications forces researchers to look for automated ways of programming and adapting these systems. Self-adapting, self-organising software system is one of the possible ways to tackle and manage higher complexity. A set of small independent problem solvers, working together in a dynamic environment, solving multiple tasks, and dynamically adapting to changing requirements is one way of achieving true self-adaptation in software systems. Our work presents a dynamic multi-task environment and experiments with a self-adapting software system. The Evolvable Virtual Machine (EVM) architecture is a model for building complex hierarchically organised software systems. The intrinsic properties of EVM allow the independent programs to evolve into higher levels of complexity, in a way analogous to multi-level, or hierarchical evolutionary processes. The EVM is designed to evolve structures of self-maintaining, self-adapting ensembles, that are open-ended and hierarchically organised. This arti...

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A New Kind of Science

Cited by 1,439 publications

References 0 publications

Spontaneous emergence of spatio-temporal order in class 4 automata

Spontaneous emergence of spatio-temporal order in class 4 automata

Between Order and Chaos: The Quest for Meaningful Information

Self-adaptation and Dynamic Environment Experiments with Evolvable Virtual Machines

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