  The origin of non-extensive thermodynamics in physical systems has been under
intense debate for the last decades. Recent results indicate a connection
between non-extensive statistics and thermofractals. After reviewing this
connection, we analyze how scaling properties of Yang-Mills theory allow the
appearance of self-similar structures in gauge fields. The presence of such
structures, which actually behave as fractals, allows for recurrent
non-perturbative calculations of vertices. It is argued that when a statistical
approach is used, the non-extensive statistics is obtained, and the Tsallis
entropic index, $q$, is deduced in terms of the field theory parameters. The
results are applied to QCD in the one-loop approximation, resulting in a good
agreement with the value of $q$ obtained experimentally.
