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 <(l) over tilde > and the anisotropy or structural match parameter in, are introduced to describe the pattern transformation. These two parameters can be predicted according to our model. Fractal patterns arise when <(l) over tilde > less than or equal to 1. Fractal patterns having a strong anisotropy (m --> 1) at relatively low surface supersaturations, and a very weak anisotropy (m--> -1) at high surface supersaturations. The results are in excellent agreement with the results of NH4Cl crystals grown from different mediums. (C) 2002 Published by Elsevier Science B.V.