Fractal to Non-Fractal Morphological Transitions in Stochastic Growth Processes

From the formation of lightning-paths to vascular networks, diverse nontrivial self-organizing and self-assembling processes of pattern formation give rise to intricate structures everywhere and at all scales in nature, often referred to as fractals. One striking feature of these disordered growth processes is the morphological transitions that they undergo as a result of the interplay of the entropic and energetic aspects of their growth dynamics that ultimately manifest in their structural geometry. Nonetheless, despite the complexity of these structures, great insights can be obtained into the fundamental elements of their dynamics from the powerful concepts of fractal geometry. In this chapter, we show how numerical and theoretical fractal analyses provide a universal description to the well observed fractal to nonfractal morphological transitions in particle aggregation phenomena.