DDLab is interactive graphics software for creating and visualizing discrete dynamical networks, and studying their behavior in terms of both space‐time patterns and basins of…
Abstract
DDLab is interactive graphics software for creating and visualizing discrete dynamical networks, and studying their behavior in terms of both space‐time patterns and basins of attraction. The networks can range from cellular automata to random Boolean networks. This article provides some general background, and gives the flavor of DDLab with a range of examples. Further details can be found at www.ddlab.comwww.ddlab.com
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Crayton C. Walker and Jaideep G. Motwani
Insights derived from the theory of complex systems and theoretical biology suggest that “small‐scale modelling” may be valuable in the construction of management theory…
Abstract
Insights derived from the theory of complex systems and theoretical biology suggest that “small‐scale modelling” may be valuable in the construction of management theory. Small‐scale modelling can be used to embed managerial perspectives in models. For that reason small‐scale modelling shows some prospect for producing what might be called inherently useful theory, namely, theory that recognizes the pragmatic limitations accompanying its use. As an example of the modelling approach, examines aspects of the management of workgroup routine. Considers directions for further research.
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Andrew Schumann and Andrew Adamatzky
The purpose of this paper is to fill a gap between experimental and abstract‐theoretic models of reaction‐diffusion computing. Chemical reaction‐diffusion computers are amongst…
Abstract
Purpose
The purpose of this paper is to fill a gap between experimental and abstract‐theoretic models of reaction‐diffusion computing. Chemical reaction‐diffusion computers are amongst leading experimental prototypes in the field of unconventional and nature‐inspired computing. In the reaction‐diffusion computers, the data are represented by concentration profiles of reagents, information is transferred by propagating diffusive and phase waves, computation is implemented in interaction of the traveling patterns, and results of the computation are recorded as a final concentration profile.
Design/methodology/approach
The paper analyzes a possibility of co‐algebraic representation of the computation in reaction‐diffusion systems using reaction‐diffusion cellular‐automata models.
Findings
Using notions of space‐time trajectories of local domains of a reaction‐diffusion medium the logic of trajectories is built, where well‐formed formulas and their truth‐values are defined by co‐induction. These formulas are non‐well‐founded set‐theoretic objects. It is demonstrated that the logic of trajectories is a co‐algebra.
Research limitations/implications
The paper uses the logic defined to establish a semantical model of the computation in reaction‐diffusion media.
Originality/value
The work presents the first ever attempt toward mathematical formalization of reaction‐diffusion processes and is built building up semantics of reaction‐diffusion computing. It is envisaged that the formalism produced will be used in developing programming techniques of reaction‐diffusion chemical media.
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Andrew Adamatzky and Genaro J. Martinez
Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space‐time configurations. No one has tried to…
Abstract
Purpose
Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space‐time configurations. No one has tried to analyze a generative power of cellular‐automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large‐scale spatially extended systems.
Design/methodology/approach
Let all but one cell be in alike state in initial configuration of a one‐dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three‐by‐three cell blocks occurred in the automaton's space‐time configuration.
Findings
The paper builds a hierarchy of generative diversity of one‐dimensional cellular automata with binary cell‐states and ternary neighborhoods, discusses necessary conditions for a cell‐state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions.
Research limitations/implications
The method developed will be used – in conjunction with other complexity measures – to built a complete complexity maps of one‐ and two‐dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity.
Originality/value
The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata.
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To program cellular automata is to define cell neighbourhood and cell‐state transition rules in order to design an automation which exhibits determined patterns in its evolution…
Abstract
To program cellular automata is to define cell neighbourhood and cell‐state transition rules in order to design an automation which exhibits determined patterns in its evolution or which transforms a given image into another image. In general, a tool for the automatic programming of cellular automata should translate the tuple (source‐configuration) → (target‐configuration) into a set of cell‐state transition rules. This is a problem which has not been completely solved yet. Attempts to show examples of automatic programming of cellular automata using identification algorithms. Results obtained can be used in the design of massively parallel processors with cellular‐automata architecture and a conventional, as well as non‐traditional (e.g. molecular and chemical), elementary base.