The Rendering Of Inside Structure And Noise Perturbed Generalized M-J Set

The nonlinear theory is a new developing frontier science which describes the complex systematic structure shape.It cantains three important concepts: Fractal, Chaos and Soliton.Here we lay a particular emphasis on the studying of the fractal structure of the generalized Mandelbrot set and Julia set, the main content are as followings:Modifies the escape-time method, analyzes the process that the points inside a period bulb of the generalized Mandelbrot set (the generalized M set) after iterating a certain pre-period process finally enter into the periodic orbit. All the points with same pre-period form a circularity structure which shapes similar as the period bulb; as pre-period grows the circularity structure diffuses towards the period bulb boundary until crams the whole period bulb. Besides, we present a particular experimental observation of the rule of the pre-period bulb graphic of the generalized M set and its growing process and offer the theory proof.Adopting the experimental mathematics method combining complex variable function theory with computer aided drawing, this paper researches on the structural characteristic and the fission-evolution law of the generalized Mandelbrot set (generalized M set in short) perturbed by composing noise of additive and multiplicative, analyzes the effect of random perturbation to the generalized M set.Contrastively researches on the structural characteristic and the fission-evolution law of four different kinds of generalized Julia set (generalized J set in short) with different parameter c, which includes the generalized J set without any perturbation, the generalized J set perturbed by additive noise, the generalized J set perturbed by multiplicative noise and the generalized J set perturbed by composing noise of additive and multiplicative, analyzes the effect of random perturbation to the generalized J set, illuminate the stability of the generalized J set.