  The perturbative approach to QCD has been shown to be limited, and the
difficulties to obtain accurate calculations in the low-energy region seems to
be insurmountable. A recent approach uses the fractal structures of Yang-Mills
Field Theory to circumvent those difficulties, allowing for the determination
of an analytic expression for the running coupling. The results obtained are in
agreement with several experimental findings, and explain many of the observed
phenomena at high-energy collisions. In this work, we address some of the
conceptual aspects of the fractal approach, which are expressed in terms of the
renormalization group equation and the self-energy corrections to the parton
mass. We associate these well-known concepts with the origins of the fractal
structure in the quantum field theory.
