Morphology of Experimental and Simulated Turing Patterns

Figure 2.1: First evidence for Turing Pattern formation in a gel-strip reactor. The reactantsdiffusion into the gel-strip from compartment on the sides (i.e. top and bottom in the image).The pictures are side-views of the Turing structures, i.e. perpendicular to the concentrationgradient in the gel-strip. (Image reproduced from Ref. [7])Castets’ gel-strip reactor the gel in Ouyang’s experiment is thinner and viewed fromthe top, which results in observable extended quasi two-dimensional Turing patterns.The dimensionality of patterns was discussed in Ref. [46], which showed that thepatterns obtained in Ref. [47] were two-dimensional. However three-dimensionalpatterns are possible for different configurations, as shown in Ref. [12]. Numericalanalysis of three-dimensional Turing patterns can be found in Ref. [58], where alsoa periodic minimal surface, the gyroid, is found as a solution. An advanced setupthat shares the same principle, the open one-sided gel disk reaction, was used inlater experiments to avoid effects of to the actual three-dimensional structure of thereactor [54]. In the case of three-dimensional Turing structures the observed quasitwo-dimensional patterns consist of the spatial average of all layers of patterns in thesystem. The occurrence of rhombic patterns, traveling waves and spatio-temporalpatterns, different from those observed in Ref. [47] has been attributed to the threedimensionalstructure of the experiment [55]. However rhombic patterns were alsopredicted for quasi two-dimensional systems [45]. A small region with a rhombicarray can even be found in the top right corner of the hexagonal pattern of Fig. 2.3and the occurrence of rhombic patterns in the CIMA reaction was further verifiedin Ref. [17].18