  The entropic measure for analysis of grey level inhomogeneity (GLI) is
proposed as a function of length scale. It allows us to quantify the
statistical dissimilarity of the actual macrostate and the maximizing entropy
of the reference one. The maximums (minimums) of the measure indicate those
scales at which higher (lower) average grey level inhomogeneity appears
compared to neighbour scales. Even a deeply hidden statistical grey level
periodicity can be detected by the equally distant minimums of the measure. The
striking effect of multiple intersecting curves (MIC) of the measure has been
revealed for pairs of simulated patterns, which differ in shades of grey or
symmetry properties, only. This indicates for a non-trivial dependence of the
GLI on length scale. In turn for evolving photosphere granulation patterns, the
stability in time of the first peak position has been found. Interestingly, at
initial steps of the evolution clearly dominates the third peak. This indicates
for a temporary grouping of granules at length scale that may belong to
mesogranulation phenomenon. This behaviour has similarities with that reported
by Consolini, Berrilli et al. (2003, 2005) for binarized granulation images of
a different data set.

Statistical Mechanics