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This paper contrastively researches the structural characteristic and the fission-evolution law of four different kinds of generalized Julia set (generalized J set in short) with different parameterc, which includes the generalized J set without any perturbation, the generalized J set perturbed by additive noises, the generalized J set perturbed by multiplicative noise, and the generalized J set perturbed by composing additive and multiplicative noises, analyzes the effect of random perturbation to the generalized J set, and illuminates the stability of the generalized J set.

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