We study whether mesogranulation flow patterns at the solar surface can arise solely from the statistical properties of granules and intergranular lanes. We have developedone- and two-dimensional models with local interaction rules between the artificial ``granules'' mimicking the actual physical processes on the solar surface. Defining mesogranulation according to the age of intergranular (downflow) lanes corresponding to the often applied ``cork method'', as well as the areas of divergence of the horizontal velocity (two-dimensional model), we find that mesogranular patterns are present in our models. Our study of the dependence of the properties of the mesogranular patterns on the model parameter and interaction rules reveals that the patterns do not possess intrinsic length and time scales.Key words: Sun: granulation
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