Toward a quantitative theory of self-generated complexity
Quantities are defined operationally which qualify as measures of complexity of patterns arising in physical situations. Their main features, distinguishing them from previously used quantities, are the following: (1) they are measure-theoretic concepts, more closely related to Shannon entropy than to computational complexity; and (2) they are observables related to ensembles of patterns, not to individual patterns. Indeed, they are essentially Shannon information needed to specify not individual patterns, but either measure-theoretic or algebraic properties of ensembles of patterns arising in a priori translationally invariant situations. Numerical estimates of these complexities are given for several examples of patterns created by maps and by cellular automata.
- Research Organization:
- Physics Dept., Univ. of Wuppertal, Wuppertal
- OSTI ID:
- 6725073
- Journal Information:
- Int. J. Theor. Phys.; (United States), Vol. 25:9
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
MEASURE THEORY
COMPLEX MANIFOLDS
QUANTUM MECHANICS
COMPUTER GRAPHICS
COMPUTERIZED SIMULATION
ENTROPY
IMAGE PROCESSING
INVARIANCE PRINCIPLES
KOLMOGOROV EQUATION
PATTERN RECOGNITION
PROGRAMMING LANGUAGES
SPACE-TIME
TOPOLOGICAL MAPPING
DIFFERENTIAL EQUATIONS
EQUATIONS
MAPPING
MATHEMATICAL MANIFOLDS
MATHEMATICS
MECHANICS
PHYSICAL PROPERTIES
PROCESSING
SIMULATION
THERMODYNAMIC PROPERTIES
TRANSFORMATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics