In this article, we report the formation of fractal structures in nickel-based alloy systems, in thin films during ion beam-solid interactions. The experimental results show that a necessary condition for the fractal growth in thin films is amorphous structural phase transition in the amorphous matrix. The fractal dimensions of the observed patterns depended on the specific alloy systems: Df = 1.4 for Ni-Zr system and Df=1.7 for Ni-Mo system. The relationship among ion-solid interaction, amorphous structural phase transition and the fractal growth in thin films is also discussed.