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The Landau-Ginzburg equations used to describe periodic spatial patterns in two dimensions are extended to a set of spatiotemporal equations. The extension is determined by the requirement that the equations of motion commute with translations, reflections, and rotations in the plane. This simple model produces a variety of complex structures similar to those observed in chemical reactions, ferrofluids, Rayleigh-B\'enard convection, and magnetic bubble materials.
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Gemunu H. Gunaratne (1993) studied this question.
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