GaN(0001) thin films are grown using radio frequency plasma assisted molecular beam epitaxy. By changing the growth temperature, anisotropic growth rate behavior is observed in both the step-flow growth mode and the 2D island growth mode. Tunneling scanning microscopy reveals, in the step-flow growth mode, strong influences from the growth anisotropy on the shape of the terrace edges, resulting in striking differences between hexagonal and cubic films. In the 2D nucleation growth mode, triangularly shaped islands are formed. The significance of growth anisotropy to growing high quality GaN films is discussed.published_or_final_versio