Abrupt transitions between large-scale grassland and desert in arid and semiarid regions have been observed in nature and reproduced by modeling studies. Observations also show the existence of nonuniform fine-scale vegetation patterns along the transition zone. This paper attempts to better understand these observations from two very different spatial scales. By explicitly introducing horizontal interaction terms into our previous dynamical grassland model, vegetation patterns with high diversities are found in the transition zone, and the system possesses an infinite number of equilibrium states in response to a given climatic forcing. The transition can be elucidated in two ways. In terms of the vegetation formations, the ecosystem undergoes the transition from uniform grassland to regular and irregular vegetation patterns, and then to pure desert as the moisture index (i.e., the ratio of precipitation over potential evaporation) decreases. In terms of biomass, the transition from grassland to desert goes through a narrow range of moisture index under which grassland is most fragile, as indicated by erratic vegetation patterns and large variation of average biomass. The existence of this range, however, has not been reported in previous modeling studies, and still needs to be validated using observational data.