  Using numerical simulations and scaling theory we study the dynamics of the
world-wide Web from the growth rules recently proposed in Ref. [1] with
appropriate parameters. We demonstrate that the emergence of power-law behavior
of the out- and in-degree distributions in the Web involves occurrence of
temporal fractal structures, that are manifested in the scale-free growth of
the local connectivity and in first-return time statistics. We also show how
the scale-free behavior occurs in the statistics of random walks on the Web,
where the walkers use information on the local graph connectivity.
