The formation of a specific lateral microstructure in membranes appears essential for a proper biological function of many biomembranes. The formation of gel domains in a fluid lipid bilayer during cooling is a simple, but perhaps the most fundamental process that results in membrane microstructure. We have quantitatively examined the nucleation and growth of gel domains in supported bilayers with a simple binary phospholipid composition. The shape and internal structure of the domains is characterized by two-photon excitation polarization fluorescence microscopy and atomic force microscopy. These studies reveal that the gel domains are polycrystalline and that the lipid chains are tilted with respect to the surfaces normal as expected for the L(beta)' phase. We find that domain nucleation is governed by defects and that nearest neighbor nucleation point distances are correlated. Furthermore, the nucleation point density increases with increased cooling rate as expected from standard nucleation theory. Advanced analysis of the fluorescence images reveals detailed information about the shape of the domains in terms of area, fractal dimension, radius of gyration, asymmetry and orientation. With an average fractal dimension of 1.8 the domains are far from circular and their shape is controlled by a combination of diffusion limited growth and line tension, rather than line tension alone or molecular organization. This implies that lipid ordering at the domain interfaces does not determine the growth rate of the domain. The growth of a domain is clearly effected by the positions of the surrounding domains. To study this effect, we generate Voronoi polygons based on the nucleation point positions. A Voronoi polygon around a nucleation point constitutes the nearest neighborhood of this point. Our analysis shows that the domain area is proportional to the corresponding polygon area, and that the principle axis of the domain orients along the principal axis of the polygon. Furthermore, the position of the domain center of mass moves from the nucleation point towards the polygon center of mass. Hence, we conclude that the positions of the nucleation points to a large extend govern the final size and orientation of the domains.