Natural patterns in nonequilibrium systems.

We discuss the theoretical description of the formation of natural cellular patterns by means of rotationally invariant order parameter equations. Starting from the hydrodynamic basic equations it turns out that the order parameter equations have nonlocal character. We present a suitable approximation scheme of the nonlocal terms by local ones which is based on a systematic gradient expansion. A truncation of this expansion leads to model equations which are widely used in the theoretical treatment of pattern formation in complex systems. Its application to spiral turbulence is studied in detail. [ABSTRACT FROM AUTHOR]