It is shown that random walks in which the set of visited points is a fractal emerge from a maximun entropy formalism applied to the generalized entropies introduced by Tsallis [J. Stat. Phys. 52, 479 (1988)], upon suitable constraints. This connection between fractals and Tsallis entropies suggests that the generalized statistical mechanics derived from the latter could provide a natural frame for studying fractally structured systems.

• Received 11 November 1993

DOI:https://doi.org/10.1103/PhysRevE.49.R956