In this paper we examine the simulation results of a fully nonlinear, three–dimensional dynamo and obtain inferences useful in the study of present and past geomagnetic field. This approach has importance because of the limitation in the available data of the real magnetic field: the present field is known with a high accuracy, but the time covered is only a small fraction of the time constant inherent to the geodynamo, while palaeomagnetic data provide data for a long time–span, but they are of poor quality and are distributed quite irregularly both in space and time. Thus, we compare what we see from the external field of the dynamo model with the features established or conjectured for the present or palaeomagnetic fields. We show that some of the statistical properties of the magnetic field generated by dynamo models compare well with those of the real magnetic field: dominance of the axial dipole, similar power in each degree of the harmonic at the core surface, nearly normal distribution of Gauss coefficients, and the lack of correlation among their variations. Differences were observed in other features, such as drift in the azimuthal direction and concentration of magnetic flux in small patches at the core surface. They can be attributed to either the shortness of the observational period, or to the difference in the resolution of the models, which suppresses small–scale features far below the level of the observation.