We estimate the minimum length on which solar granulation can be considered to
be a Markovian process. We measure the variation in the bright difference
between two pixels in images of the solar granulation for different distances
between the pixels. This scale-dependent data is empirically analyzed to find
the minimum scale on which the process can be considered Markovian. The results
suggest that the solar granulation can be considered to be a Markovian process
on scales longer than r_M=300-500 km. On longer length scales, solar images can
be considered to be a Markovian stochastic process that consists of structures
of size r_M. Smaller structures exhibit correlations on many scales simultaneously yet cannot be described by a hierarchical cascade in scales. An
analysis of the longitudinal magnetic flux density indicates that it cannot be
a Markov process on any scale. The results presented in this paper constitute a
stringent test for the realism of numerical magneto-hydrodynamical simulations
of solar magneto-convection. In future exhaustive analyse, the non-Markovian
properties of the magnetic flux density on all analyzed scales might help us to
understand the physical mechanism generating the field that we detect in the solar surface.