  The dynamics of units (molecules) with slowly relaxing internal states is
studied as an iterated function system (IFS) for the situation common in e.g.
biological systems where these units are subjected to frequent collisional
interactions. It is found that an increase in the collision frequency leads to
successive discrete states that can be analyzed as partial steps to form a
Cantor set. By considering the interactions among the units, a self-consistent
IFS is derived, which leads to the formation and stabilization of multiple such
discrete states. The relevance of the results to dynamical multiple states in
biomolecules in crowded conditions is discussed.

Soft Condensed Matter;Statistical Mechanics;Adaptation and Self-Organizing Systems