Electron Excitation Dynamics, Localization, and Solvation in Small Clusters

of a straight line is unity (Table II), this suggest that the branching multiplicity goes as the radial distance to the 0.7 power. We close by noting that the presently popular parameter fractal dimension tells us little about the true visual richness of form in even the most simplistic of cases. We further illustrate this conclusion by the following example. We assume that a simple curve having some given constant width defines the elementary topology of a two-dimensional cluster, and we calculate its intrinsic dimension defined by the relationship of cluster mass M to radial extent R; Le., log (M) = D log ( R ) (Table 11). We note that this intrinsic dimension would not distinguished between radially diverging straight lines and the equiangular spiral (intrinsic dimension equal to unity) or between an Archimedian spiral and a solid circle (intrinsic dimension equal to two). Also, it seems strange to presuppose that examples having the same fractal dimension would have much in common concerning their form (as well as their growth). And yet, such practice is adopted in current literature. A similar conclusion has been reached by Hoover.30 He states: “It is clear that the fractal dimensionality is a far-from-complete description of geometry. Both a smooth two-dimensional surface and a Brownian trajectory in three-dimensional space have the same fractal dimensionality, but they are very different from the geometric point of view.”