The appearance of traveling wave states in translationally invariant systems is well-understood, and such states have been observed in a number of fluid systems. A stationary, symmetric ordered pattern undergoes a symmetry-breaking bifurcation producing a nonsymmetric pattern which propagates uniformly in either characteristic direction.
In circularly-symmetric systems such states have uniformly rotating rings of cells. Individual cells within the rotating rings assume an asymmetric shape which depends on the direction of rotation.
2 Cell Rotating
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11/2 Rotating
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11/1 Rotating
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