Morphology and selection processes in diffusion-controlled growth patterns

The evolution and selection of fractal and compact growth patterns is described. As a particular example the growth of a supercritical nucleus occurring during typical first-order phase transitions and its behaviour at long times and large lengths is discussed. While the generic growth mode is the dendritic growth, we discuss also the recently discovered doublon-growth in two dimensions and the occurrence of fractal growth at low driving forces. Finally numerical and analytical results on the competition of two or more growth patterns along a growth front are presented.