Fractal growth by local sensitive epidemic model (LSEM) simulating the internal feeding systems (IFS)

The fractal systems may be classified into two families which are distinguishable by a different nutrient feeding during their growth process. For the internal feeding systems (IFS), the source is directly connected to the growing interface, while for the external feeding systems (EFS) it is placed far away so that the released particles have to execute random walks before adhering to the aggregate. A generalized model, nicknamed local sensitive epidemic model (LSEM) is developed to unify the main models simulating the growth of the IFSystems, by combining all their growth parameters (GP) and growth rules (GR). This model considers in addition: (i) a particle interaction extended to the kth neighbour, which may be attractive or repulsive; (ii) a continuous updating of the local characteristics of the surrounding medium; and (iii) an aggregate relaxation which tends to optimize the total energy during or after the growth process. The coupled effects of all these parameters allow one to simulate the main fractal phases observed experimentally, and to discuss the conditions under which they may be obtained as well as their different morphological transitions.