  Critical systems have always intrigued physicists and precipitated the
development of new techniques. Recently, there has been renewed interest in the
information contained in their classical configurations, whose computation do
not require full knowledge of the wavefunction. Inspired by holographic
duality, we investigated the entanglement properties of the classical
configurations (snapshots) of the Potts model by introducing an ansatz ensemble
of random fractal images. By virtue of the central limit theorem, our ansatz
accurately reproduces the entanglement spectra of actual Potts snapshots
without any fine-tuning of parameters or artificial restrictions on ensemble
choice. It provides a microscopic interpretation of the results of previous
studies, which established a relation between the scaling behavior of snapshot
entropy and the critical exponent. More importantly, it elucidates the role of
ensemble disorder in restoring conformal invariance, an aspect previously
ignored. Away from criticality, the breakdown of scale invariance leads to a
renormalization of the parameter $\Sigma$ in the random fractal ansatz, whose
variation can be used as an alternative determination of the critical exponent.
We conclude by providing a recipe for the explicit construction of fractal unit
cells consistent with a given scaling exponent.
