Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.
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