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The dynamics of units (molecules) with slowly relaxing internal states isstudied as an iterated function system (IFS) for the situation common in e.g.biological systems where these units are subjected to frequent collisionalinteractions. It is found that an increase in the collision frequency leads tosuccessive discrete states that can be analyzed as partial steps to form aCantor set. By considering the interactions among the units, a self-consistentIFS is derived, which leads to the formation and stabilization of multiple suchdiscrete states. The relevance of the results to dynamical multiple states inbiomolecules in crowded conditions is discussed.Comment: 7 pages, 7 figures. submitted to Europhysics Letter

Inter–Intra Molecular Dynamics as an Iterated Function System