In the field of image simulation, to assess the information content of images, it is necessary to correctly model both objects and backgrounds. This requirement is particularly required to assess the characteristics of images to be generated by future observation instruments, as is the case in earth observation and remote sensing. The physical correction of the models depend basically on the final resolution. Stochastic analysis is a powerful tool to solve problems in domains where deterministic solutions are not satisfactory. There is thus a need to develop efficient and accurate simulation techniques for multidimensional random fields. The turning bands method (TBM) has been used in geophysical sciences, in hydrology, and more recently in remote sensing to simulate medium and large scale data fields, and it can be used to represent realistic topographic surfaces or radiometric nonuniformities induced by unknown factors such as soil thickness of moisture. We present and illustrate two generalizations of the TBM. In the first, we add fractal concepts to the method, thus enabling the synthesis of a 2D stochastic field with a specified fractal dimension. In the second, we extend the TBM to generate nonisotropic fields, which do occur in many fields, in particular in earth resources modeling and classification.