Study on Fractal Characteristics in the e${}^{+}$e${}^{-}$ Collisions at $\sqrt{s_{NN}}=250$GeV

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.