In this work, it is discussed quadrilateral mesh generation using patterns of domain decomposition. Mesh generation is treated on domains delimited by two, three and four curves. Patterns of domain decomposition are applied to domains that satisfy a set of conditions called essential conditions. However, the approach developed can be applied to other domain topologies. Mesh generation begins with an initial domain decomposition, each subdomain also is independently decomposed until all the subdomains enable mesh generation using bilinear mapping. The decomposition is done by creating fictitious internal curves that demarcate the subdomains. These curves can intersect giving rise to points of intersection, which are called geometric parameters and can be varied to change the geometry of the subdomains in order to improve the quality of the generated mesh. The subdomains are bounded by curves, which have a defined number of subdivisions, this will be called topological parameters and of whose values depend the type of decomposition applied on subdomains. Patterns of decomposition were designed giving way to patterns of mesh generation that have values set for its geometric and topological parameters, in this way is possible to know the topology and the level of hierarchical decomposition a priori. Topological parameters were dynamically varied to show the possibility of finding various mesh topologies on a domain. Examples are included to show the applicability of the proposed methodology.