A stochastic model is presented that simulates cloud cover. Implementations reaching from the simple simulation of the steady state probability distribution of cloud cover up to the generation of cloud cover as a function of time are shown. In the model, the steady state probability distribution of cloud cover is invariant to the observation area over a wide range. Simulation results are discussed and compared with real world data. Particularly, the steady state probability distributions compare well with the real world. (C) 2011 Elsevier Ltd. All rights reserved.