In this paper we study and compare critical Markov random fields (CMRFs) and fractional Brownian motions (FBMs). Both of these classes of models can be used to describe self-similar phenomena. Their characteristics, namely the index of similarity of a FBM, and the critical exponents of a CMRF, are defined and contrasted. We argue that CMRFs provide a more flexible mechanism for generating self-similar patterns, since the parameters of a CMRF can be selected to generate anisotropic patterns, while FBM models are inherently isotropic.
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