A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such a fractal. Its Haussdorf dimension and its Lipshitz-Hölder exponent are determined in terms of the entropic index $q$. The connections with the intermittency in experimental data are discussed. The thermodynamical aspects of the thermofractal is related to the microscopic interaction of its components through the $S$-matrix.

• Received 19 January 2016

DOI:https://doi.org/10.1103/PhysRevD.93.054001