Download (1.6 MB)
Reconstructability analysis is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss (reduction in constraint) into lower ordinality relations. Set-theoretic reconstructability analysis (SRA) is used to characterize the mappings of elementary cellular automata. The degree of lossless decomposition possible for each mapping is more effective than the λ parameter (Walker & Ashby, Langton) as a predictor of chaotic dynamics.
Complete SRA yields not only the simplest lossless structure but also a vector of losses of all decomposed structures, indexed by parameter, τ. This vector subsumes λ, Wuensche’s Z parameter, and Walker & Ashby’s “fluency” and “memory” parameters within a single framework, and is a strong but still imperfect predictor of the dynamics: less decomposable mappings more commonly produce chaos. The set-theoretic constraint losses are analogous to information distances in information-theoretic reconstructability analysis (IRA). IRA captures the same information as SRA, but allows λ, fluency, and memory to be explicitly defined.
Martin Zwick was awarded his Ph.D. in Biophysics at MIT in 1968, and joined the Biophysics Department faculty of the University of Chicago in 1969. Initially working in crystallography and macromolecular structure, his interests shifted to systems theory and methodology, the field now known as the study of chaos, complexity, and complex adaptive systems. Since 1976 he has been teaching and doing research in the Systems Science PhD Program at Portland State University; during the years 1984-1989 he was director of the program.
His main research areas are information theoretic modeling, machine learning, theoretical biology, game theory, and systems theory and philosophy. Scientifically, his focus is on applying systems theory and methodology to the natural and social sciences, most recently to biomedical data analysis, the evolution of cooperation, and sustainability. Philosophically, his focus is on how systems ideas relate to classical and contemporary philosophy, how they offer a bridge between science and religion, and how they can help us understand and address societal problems.
System design, System analysis, Cellular automata -- Mathematical models, Reconstructability analysis, Chaotic behavior in systems -- Mathematical models
Dynamical Systems | Theory, Knowledge and Science
© Copyright the author(s)
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
The purpose of this statement is to help the public understand how this Item may be used. When there is a (non-standard) License or contract that governs re-use of the associated Item, this statement only summarizes the effects of some of its terms. It is not a License, and should not be used to license your Work. To license your own Work, use a License offered at https://creativecommons.org/
Zwick, Martin and Shi, Hui, "Reconstructability Analysis of Elementary Cellular Automata" (2010). Systems Science Friday Noon Seminar Series. 38.