Information-theoretic model of self-organizing fullerenes and the emergence of C60

Highlights: • Information-theoretic model of self-organizing fullerenes end-directed- evolution towards C_60. • Emergence of C₆₀ described by fractal dimensional analysis. • Self-organizing fullerenes modelled as dissipative dynamical systems. • Larger cages' transform into smaller ones. • The density variation of cages used to calculate transformations probabilities. • Shannon entropy is evaluated to calculate Fractal Dimension of all cages. 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 $\mathrm{cage}\to cage$ transformations are used to evaluate Shannon entropies for every carbon cage. Fractal dimension of the cages are calculated from their respective entropies. C₆₀ 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.