Abstract: This paper develops a new framework to characterize small-scale patterns. The core idea is to formulate the problem of modeling small-scale patterns by sequential minimizing energy functionals in Sobolev spaces, leading to a sequence of eigenvalue problems. Mathematical analysis on the structure of the small-scale pattern at each level and the convergence behavior of the proposed model are explored in detail. We obtain a novel effective, adaptive, and hierarchical image representation. And the model will benefit applications such as image synthesis and computational visual perception. Numerically, small-scale patterns can be easily computed by eigenvalue decompositions of sparse, symmetric matrices.