Abstract
Dendritic crystal growth is one of the most typical phenomena of the spontaneous pattern formation in nature. In order to understand these phenomena in macroscopic level, simple phase field models for one component melt growth are presented. These models are written by the system of partial differential equations which is called reaction diffusion systems. They include thermo-dynamical driving force, surface tension and anisotropy as local dynamics, and temperature field as non-local effect. They can simulate the formation of various dendritic patterns in both two dimensional and three dimensional spaces. Some qualitative relations between the shapes of crystals and some physical parameters are discussed.
