Numerous computational methods for generating and simulating binary and grey-level natural digital-image textures are proposed using a variety of stochastic models. Pictorial results of each method are given and various aspects of each approach are discussed. The quality of the natural texture simulations depends on the computation time for data collection, computation time for generation, and storage used in each process. In most cases, as computation time and data storage increase, the visual match between the texture simulation and the parent texture improves. Many textures are adequately simulated using simple models thus providing a potentially great information compression for many applications.