Self-epitaxial nucleation origin of fractal aggregation

The self-epitaxial nucleation and growth origin of the formation and transformation of crystalline fractal pattern is identified for the first time. Two universal parameters, so-called relative elemental branching period 〈l̃〉 and the anisotropy or structural match parameter m, are introduced to describe the pattern transformation. These two parameters can be predicted according to our model. Fractal patterns arise when 〈l̃〉⩽1. Fractal patterns have a strong anisotropy (m→1) at relatively low surface supersaturations, and a very weak anisotropy (m→−1) at high surface supersaturations. The theoretic results are in excellent agreement with experiments.