MORPHOLOGICAL CHARACTERIZATION OF PATTERNS IN REACTION-DIFFUSION SYSTEMS

Morphological measures for spatial patterns occuring as dissipative st ructures in systems driven far from equilibrium are introduced. They c haracterize the geometry and topology of the patterns and are capable to distinguish irregular structures with respect to the morphology. In particular, we analyze turbulent and regular patterns (Turing pattern s) in chemical reaction-diffusion systems observed in a tyro-dimension al open gel reactor with a chlorite-iodide-malonic acid reaction. Intr oducing the concept of level contours, the measures turn out to be pol ynomials of low order (cubic and fourth degree) in the grey-scale leve l of the images. Thus the dependence on the experimental conditions is reflected only in a finite number of coefficients, which can be used as order parameters for the morphology of patterns. We observe a symme try breaking of the polynomials when the type of the pattern changes f rom hexagons to turbulence or stripes. Therefore it is possible to des cribe the pattern transitions quantitatively and it may be possible to classify them in a similar way like thermodynamic phase transitions.