Morphological characterization of patterns in reaction-diffusion systems

Morphological measures for spatial patterns occuring as dissipative structures in systems driven far from equilibrium are introduced. They characterize 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 patterns) in chemical reaction-diffusion systems observed in a two-dimensional open gel reactor with a chlorite-iodide-malonic acid reaction. Introducing the concept of level contours, the measures turn out to be polynomials of low order (cubic and fourth degree) in the grey-scale level 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 symmetry breaking of the polynomials when the type of the pattern changes from hexagons to turbulence or stripes. Therefore it is possible to describe the pattern transitions quantitatively and it may be possible to classify them in a similar way like thermodynamic phase transitions.