Fractality \`a la carte: a general particle-cluster aggregation model

Abstract

Aggregation phenomena are ubiquitous in nature, encompassing out-of-equilibrium processes of fractal pattern formation, important in many areas of science and technology. Despite their simplicity, foundational models such as diffusion-limited aggregation (DLA) or ballistic aggregation (BA), have contributed to reveal the most basic mechanisms that give origin to fractal structures. Hitherto, it has been commonly accepted that, in the absence of long-range particle-cluster interactions, the trajectories of aggregating particles, carrying the entropic information of the growing medium, are the main elements of the aggregation dynamics that determine the fractality and morphology of the aggregates. However, when interactions are not negligible, fractality is enhanced or emerges from the screening effects generated by the aggregated particles, a fact that has led to believe that the main contribution to fractality and morphology is of an energetic character only, turning the entropic one of no special significance, to be considered just as an intrinsic stochastic element. Here we show that, even when long-range attractive interactions are considered, not only screening effects but also, in a very significant manner, particle trajectories themselves are the two fundamental ingredients that give rise to the fractality in aggregates. We found that, while the local morphology of the aggregates is determined by the interactions, their global aspect will exclusively depend on the particle trajectories. Thus, by considering an effective aggregation range, we obtain a wide and versatile generalization of the DLA and BA models. Furthermore, for the first time, we show how to generate a vast richness of natural-looking branching clusters with any prescribed fractal dimension, very precisely controlled.