Yang-Mills fields present scale invariance, what allows the theory to be renormalized. In this talk we show that fractal structures can be formed by fields described by this theory. Such fractal structure allow for recursive equations that enable the calculation of high order perturbative calculations. In addition, it leads to  power-law distributions of energy and momentum, and therefore explains the emergence of the non extensive Tsallis statistics in high energy physics and in hadron physics. Similarities with the concept of thermofractal, recently introduded, are discussed, as well as comparison with experiments.