The Mycielski method is a prospering prediction algorithm which is based on searching and finding largest repeated binary patterns. It uses infinite-past data to devise a rule based prediction method on a time series. In this work, a novel two-dimensional (image processing) version of the Mycielski algorithm is proposed. Since the dimensionality definition of “past” data increases in two-dimensional signals, the proposed algorithm also needs to handle how the boundaries of the pixel cliques are iteratively extended in the neighborhood of a current pixel. The clique extension invokes novel similarity search strategies that depend on the chosen physical distance metric. The proposed prediction algorithm is used for predictive image compression and performance comparisons with other predictive coding methods are presented.