Exact Mapping from Singular Value Spectrum of Fractal Images to   Entanglement Spectrum of One-Dimensional Quantum Systems
  We examine the snapshot entropy of general fractal images defined by their singular values. Remarkably, the singular values for a large class of fractals are in exact correspondence with the entanglement spectrum of free fermions in one dimension. These fermions allow for a holographic interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the Calabrese-Cardy formula. However, the coarse-grained entropy exhibits a linear scaling due to the degeneracy of the spectrum, in contrast with the logarithmic scaling behavior in one-dimensional quantum near-critical systems. 
Ching Hua Lee, Yuki Yamada, Tatsuya Kumamoto, and Hiroaki Matsueda
cond-mat.stat-mech hep-th