Fractal properties of homologous series of structures

Abstract

The concept of lattice-graph generation considered earlier (S. EI-Basil, J. Chem. Soc., Faraday Trans. 1993, 89, 909) has been studied further. It is demonstrated, using methods of symbolic dynamics and block-renaming, that the sequence which defines these graphs is a fractal, while the generation operation bears remarkable similarity to the various stages of the Cantor dust. Furthermore, Kekulé counts of several homologous series of quasicrystal-like benzenoids form mathematical structures which possess the scaling properties of fractals. Self-similarity is extended to other homologous series of graphs (which represent chemical species) and it is demonstrated in all cases that the golden mean (τ= 1.618033989) is their characteristic scaling factor.