  We have investigated formation of structures of Rydberg atoms excited from a
disordered gas of ultracold atoms, using rate equations for two-photon Rydberg
excitation in a single atom without eliminating the intermediate state. We have
explored the validity range of these rate equations and defined a simple
measure to determine, whether our model is applicable for a given set of laser
parameters. We have applied these rate equations in Monte Carlo simulations of
ultracold gases, for different laser beam profiles, and compared these
simulations to experimental observations and find a general agreement.
