One of the most universal phenomena in embryological morphogenesis is
the formation of domains of morphologically polarized (apico-basally e
longated) epithelial cells. It has been observed that cell polarizatio
n precedes many ''obvious'' events in embryogenesis, such as invaginat
ion and evagination, folding and curling of cell sheets, differentiati
on of cells in eye development, emergence of skin derivates, and even
the budding in Marine Hydrozoa. Domains of polarized and unpolarized c
ells form ''reliefs'' in epithelial sheets that are the pre-patterns t
o the above-mentioned patterns. This paper gives a model for the pigme
nt pattern formation in animal coatings. The model simulates cell pola
rization as a co-operative self-organized process of cells in an epith
elial sheet. It is based upon the following experimentally proven prop
erties of cells and their interactions: (i) each individual cell in an
epithelial tissue is able to change shape from unpolarized to polariz
ed and back. the transition being the ''all or none'' type (both forms
are the only stable ones); (ii) polarization is transmitted from cell
to cell via their contacts; (iii) local polarization forces generate
tangential elastic tensions throughout the surrounding unpolarized cel
ls which, in turn, inhibit further polarization, thus establishing a n
egative feedback mechanism. These two types of force form the basis of
the model, which is referred to as the PE model (polarization-elastic
ity) for brevity.