  Both three- and one-dimensional studies of local multiplicity fluctuations in
hadronic Z decay are performed using data of the L3 experiment at LEP. The
normalized factorial moments in three dimensions exhibit power-law scaling,
indicating that the fluctuations are isotropic, which correspends to a
self-similar fractal. A detailed study of the corresponding one-dimensional
moments confirms this conclusion. However, two-jet subsamples have anisotropic
fluctuations, correspending to a self-affine fractal. These features are, at
least qualitatively, reproduced by the Monte Carlo models \JETSET and \HERWIG.
