the cellular automata method has been used to simulate the pattern formation of the schlögl model as a bistable reaction-diffusion system. both microscopic and macroscopic cellular automata approaches have been considered and two different methods for obtaining the probabilities in the microscopic approach have been mentioned. the results show the tendency of the system towards the more stable ...

A quasi-potential approximation to the Navier–Stokes equation for low-viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating regions of instability to either of the driving frequencies is explicitly obtained, and compared with experiments involving a frequency ratio of 1/2. The proced...

Hypotheses about the origin of vegetation pattern formation in semi-arid areas around the world almost all include a common feature of semi-arid areas: the presence of a positive feedback between plant density and water infiltration. We investigate whether this positive feedback and the spatial redistribution of runoff water are sufficient to explain vegetation pattern formation. For this purpo...

The power of genetics has been clearly demonstrated in studies of embryonic development. Systematic searches for mutant phenotypes during embyogenesis in Drosophila (Nusslein-Volhard and Wieschaus, 1980; Johnston and NussleinVolhard, 1992; Wieschaus, 1996) and zebrafish (Grunwald and Eisen, 2002) have uncovered most of the genes controlling embryonic pattern formation. The number of genes invol...