CHARACTERIZATION OF SYMMETRY PROPERTIES OF PATTERNS BY GENERALIZED AUTOCORRELATION FUNCTIONS

A generalization of autocorrelation functions is proposed, by which sy mmetry properties of spatial patterns can be measured. Such symmetry a utocorrelation functions can in particular be useful for the quantitat ive characterization of the complexity of individual patterns obtained from experiments or numerical simulations. They allow a measurement o f the degrees of symmetry by evaluating the correlation between a tran sformed pattern and the original. Experimental and numerical examples of patterns, which evolve in nonlinear optical feedback systems are ex amined.