An information-theoretic model describes the dissipative dynamical systems composed of ensembles of fragmenting, self-organizing fullerenes. The probabilities derived from the variations of the fullerene number densities that occur during cage -> cage transformations are used to evaluate Shannon entropies for every carbon cage. Fractal dimension of the cages are calculated from their respective entropies. C-60 is shown to emerges as the end-directed evolution of dynamical systems of four different ensembles of fullerenes. The information generating, transforming cages of carbon provide a perspective to evaluate the self-organizational behavior of dissipative structures.