Toward a quantitative theory of self-generated complexity Export

@article{Grassberger86a, abstract = {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 measuretheoretic 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 ina priori translationally invariant situations. Numerical estimates of these complexities are given for several examples of patterns created by maps and by cellular automata.}, author = {Grassberger, Peter}, citeulike-article-id = {5947777}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/BF00668821}, doi = {10.1007/BF00668821}, journal = {International Journal of Theoretical Physics}, keywords = {file-import-09-10-16, timeseries}, number = {9}, pages = {907--938}, posted-at = {2009-10-16 01:05:17}, priority = {2}, title = {Toward a quantitative theory of self-generated complexity}, url = {http://dx.doi.org/10.1007/BF00668821}, volume = {25}, year = {1986} }

TY - JOUR ID - Grassberger86a L3 - citeulike-article-id:5947777 N2 - 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 measuretheoretic 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 ina priori translationally invariant situations. Numerical estimates of these complexities are given for several examples of patterns created by maps and by cellular automata. IS - 9 JF - International Journal of Theoretical Physics EP - 938 TI - Toward a quantitative theory of self-generated complexity VL - 25 SP - 907 KW - file-import-09-10-16 KW - timeseries AU - Grassberger, Peter PY - 1986/// UR - http://dx.doi.org/10.1007/BF00668821 ER -