  In this work we analyse how scaling properties of Yang-Mills field theory
manifest as self-similarity of truncated n-point functions by scale evolution.
  The presence of such structures, which actually behaves as fractals, allow
for recurrent non-perturbative calculation of any vertex. Some general
properties are indeed independent of the perturbative order, what simplifies
the non-perturbative calculations. We show that for sufficiently high
perturbative orders a statistical approach can be used, the non extensive
statistics is obtained, and the Tsallis index, $q$, is deduced in terms of the
field theory parameters. The results are applied to QCD in the one-loop
approximation, where $q$ can be calculated, resulting in a good agreement with
the value obtained experimentally. We discuss how this approach allows to
understand some intriguing experimental findings in high energy collisions, as
the behavior of multiplicity against collision energy, long-tail distributions
and the fractal dimension observed in intermittency analysis.
