  Superficial (two dimensional) crack patterns appear when a thin layer of
material elastically attached to a substrate contracts. We study numerically
the maturation process undergone by these crack patterns when they are allowed
to adapt in order to reduce its energy. The process models the evolution in
depth of cracks in geological formations and in starch samples (`columnar
jointing'), and also the time evolution (over thousands of years) of crack
patterns in frozen soils. We observe an evolution towards a polygonal pattern
that consist of a fixed distribution of polygons with mainly five, six and
seven sides. They compare very well with known experimental examples. The
evolution of one of these `mature' patterns upon reduction of the degree of
contraction is also considered. We find that the pattern adapts by closing some
of the cracks and rearranging those in the immediate neighborhood. This
produces a change of the mean size of the polygons, but remarkably no changes
of the statistical properties of the pattern. Comparison with the same behavior
recently observed in starch samples is presented.
