Dynamical systems of objects following any set of rules will evolve
over time. Studying ways of describing this evolution, especially in order
to make meaningful generalizations about what to expect in the long run, is
the study of pattern formation.
One of the key problems in pattern formation is the role of noise.
Noise can be interpreted as random differences in the initial conditions,
random fluctuation of parameters and even random system adherence to the
rules. Typically, noise can be expected to disrupt an expectedpattern
but sometimes (for example, this is the case with Turing systems) noise can
actually be necessary or helpful for generating and stabilizing a pattern.
In any patterning mechanism, is it important to recognize whether
the patterning is directed or self-organized: