  Despite simplicity, the synchronous cellular automaton [D.A. Young, Math.
Biosci. 72, 51 (1984)] enables reconstructing basic features of patterns of
skin. Our extended model allows studying the formatting of patterns and their
temporal evolution also on the favourable and hostile environments. As a
result, the impact of different types of an environment is accounted for the
dynamics of patterns formation. The process is based on two diffusible
morphogens, the short-range activator and the long-range inhibitor, produced by
differentiated cells (DCs) represented as black pixels. For a neutral
environment, the extended model reduces to the original one. However, even the
reduced model is statistically sensitive to a type of the initial distribution
of DCs. To compare the impact of the uniform random distribution of DCs
(R-system) and the non-uniform distribution in the form of random
Gaussian-clusters (G-system), we chose inhibitor as the control parameter. To
our surprise, in the neutral environment, for the chosen inhibitor-value that
ensures stable final patterns, the average size of final G-populations is lower
than in the R-case. In turn, when we consider the favourable environment, the
relatively bigger shift toward higher final concentrations of DCs appears in
the G. Thus, in the suitably favourable environment, this order can be
reversed. Furthermore, the different critical values of the control parameter
for the R and the G suggest some dissimilarities in temporal evolution of both
systems. In particular, within the proper ranges of the critical values, their
oscillatory behaviours are different. The respective temporal evolutions are
illustrated by a few examples.
