Newton Transform Mandelbrot-Julia Sets And Multiple Chaos Encryption

Non-linear theory contains three important concepts: Fractal, Chaos and Soliton. The theory of these concepts makes up of theoretical basis of non-line. This thesis discussed some important problems, modeling and showing M-J Set of Newton's method, utilizing trap technique to construct virtual three-dimension Newton transform Mandelbrot-Julia sets, and designing the practical algorithm of switch control chaos pseudo random bit generator.Newton's method for finding a real or complex root of function is very efficient near a simple root because the algorithm converges quadratically in the neighborhood of such a root. However, at a multiple root, it only converges linearly. Various modifications of Newton's method have been proposed in practice. In this paper create and study the generalized Newton transform J-Set, dynamic parameter and asynchronous Newton's method, analyze the effect of error and dynamic parameter. The Julia set of third-order simplified Newton' method contains the structure of classical Mandelbrot set. The multiple root attraction regions of these kinds of Julia sets are sensitive. There is not simple root attraction region in relax methodIn the following, through combining the orbit render and Newton's method, extend the Pickover and Calson trap technique, construct and study more generalized polynomial's 3D M-Set, generalizes orbit render technique. It always is found that there is standard Mandelbrot structure in the 3D M-set, which is formed by "bad" points. In M-J set, there is various 3D self-similarity color cell that corresponds with the shape of trap unit. All of results of fractal above-mentioned have been published or accepted by the journal.The traditional single may exist potential insecurity caused by intelligent methods to extract useful information from chaotic orbits. This paper introduces a method that generate pseudo random key stream by switch multiple chaoses. By this way, the randomicity and system security will be better than before. And if use parallel compute hardware, the speed of encrypt should be improved sharply.