  A model for the generation of fractal growth networks in Euclidean spaces of
arbitrary dimension is presented. These networks are considered as the spatial
support of reaction-diffusion and pattern formation processes. The local
dynamics at the nodes of a fractal growth network is given by a nonlinear map,
giving raise to a coupled map system. The coupling is described by a matrix
whose eigenvectors constitute a basis on which spatial patterns on fractal
growth networks can be expressed by linear combination. The spectrum of
eigenvalues the coupling matrix exhibits a nonuniform distribution that is
reflected in the presence of gaps or niches in the boundaries of stability of
the synchronized states on the space of parameters of the system. These gaps
allow for the selection of specific spatial patterns by appropriately varying
the parameters of the system.
