  We study the non-extensive Tsallis statistics and its applications to QCD and
high energy physics, and analyze the possible connections of this statistics
with a fractal structure of hadrons. Then, we describe how scaling properties
of Yang-Mills theories allow the appearance of self-similar structures in gauge
fields, which actually behave as fractals. The Tsallis entropic index, $q$, is
deduced in terms of the field theory parameters, resulting in a good agreement
with the value obtained experimentally.
