We present an algorithm based on texture synthesis that allows simulating a random field accounting for multiple point statistics and conditioning to hard data. The algorithm proceeds by using a fixed search neighborhood and an ordered path to visit the nodes to be simulated in a lattice. Reproduction of multiple point statistics is ensured for patterns contained within the search neighborhood. Conditioning is achieved by combining this fixed neighborhood with a larger one that looks for hard data and modifies the conditional distribution if necessary. The technique is illustrated with several examples and we discuss further avenues of research.