  The fractal characteristics of multi-particle final state are first studied
in the $e^+e^-$ collision of $\sqrt{s_{NN}}=250$GeV, with the MC simulation
generator Jetset7.4 and Herwig5.9. The result is shown that this multi-particle
final state is self-affine fractal, and exists a double-Hurst-exponent
phenomenon. Their fractal indices and the effective fluctuation strength are
also predicted.
