Inferring Statistical Complexity

James P. Crutchfield and Karl Young
Physics Department
University of California
Berkeley, California 94720, USA

ABSTRACT: Statistical mechanics is used to describe the observed information processing complexity of nonlinear dynamical systems. We introduce a measure of complexity distinct from and dual to the information theoretic entropies and dimensions. A technique is presented that directly reconstructs minimal equations of motion from the recursive structure of measurement sequences. Application to the period-doubling cascade demonstrates a form of super-universality that refers only to the entropy and complexity of a data stream.

J. P. Crutchfield and K. Young, "Inferring Statistical Complexity", Physical Review Letters 63 (1989) 105-108. [pdf]= 1,206kb zipped [pdf]= 962kb.