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Session Q02 - Mechanisms for Pattern Formation.
Invited session, Friday morning, March 24, 8:00
Ballroom A2, San Jose Convention Center
In a 1952 paper entitled The Chemical Basis of Morphogenesis Alan Turing predicted that spatial patterns can spontaneously form in a reaction-diffusion system as a control parameter is varied. The Turing instability has now been observed in laboratory experiments on a chlorite-iodide-malonic acid reaction in thin gel layers: there is a well-defined transition as a function of chemical concentration from the spatially uniform state to a hexagonal pattern. Q. Ouyang and H. L. Swinney, Nature 352, 610 (1991); G. H. Gunaratne, Q. Ouyang, and H. L. Swinney, Phys. Rev. E 50, 2208 (1994). The patterns arise solely from reaction and diffusion processes since the gel prevents convective motion. Beyond the onset of instability there are transitions to rhombic, striped, and zig-zag patterns, and in some concentration ranges the patterns become chaotic in space and time. A search for Turing patterns in another reaction (ferrocyanide-iodate-sulfite) has revealed instead another type of instability: a chemical front becomes unstable and evolves into a lamellar pattern. In addition, for some concentration range in this reaction, self-replicating spots are observed to form and undergo a continuous process of birth through replication and death through overcrowding. and H. L. Swinney, Science 261, 192 (1993); K. J. Lee, W. D. McCormick, H. L. Swinney, and J. Pearson, Nature 369, 215 (1994). Qualitatively similar stationary (Turing) patterns and replicating spot patterns are found in simple reaction-diffusion models.