Research On The Structure Characteristics Of General M-J Sets And Realization Of Its Visualization Technique

Fractal theory is a quite active part of the nonlinear science, whose research object is rough and anomalous geometry which appears in the nature and nonlinear system. Its development is very rapid and new productions emerge in endlessly. The complex and flowery fractal images drawn using fractal formulas on computer can impact the people's vision, stimulate their imagination and inspiration. The fractal images designs become an independent and important research direction in art design field.As an important part of fractal images, the general M-J sets are images which are generated by iterating of complex mappings on the complex plane. The fractal images from the general M-J sets are the most outstanding and famous.In order to research the structure characteristics better, the general M-J sets needs to be changed into intuitionistic images by using the visualization technique. The usual method of drawing general M-J sets'images is the time-escaped algorithm. The color of images drawn by the traditional time-escaped algorithm is relatively single, so the images can't represent the structure characteristics of M-J sets better, or from the view of people's aesthetic standard they don't look beautiful and can't be applied in the general range.Aimed at the problems above, the thesis researches and compares the structure of M-J sets and the relations between them based on analyzing various generating algorithms of M-J sets fractal images. New methods of color design have been advanced founded on these comparative analyses, thereby showing different structure characteristics of general M-J sets and gaining more beautiful images.The main content of the dissertation is as follows:(1) Introduces the creation and development course of fractal theory as well as its influences on relative scopes such as computer graphics and scientific visualization, summarizes the present situation of fractal theory and its application. Expounds the definitions, mathematical theory basis and relationships of M-sets, J-sets and general M-J sets. Sums up the relative research findings and structure characteristics of M-J sets using existent generating algorithms.(2)Studies the visualization technique of general M-J sets. According to the concept of visualization, the key of images visualization consists in their characteristic data and generating algorithms. The paper researches the characteristic data of generating M-J sets images, that is, complex mappings'parameters of images. Based on this research, applicable and improved visualization methods are brought forward aiming at common generating visualization algorithms and technique of general M-J sets including the time-escaped algorithm, Newton method and trap technique, along with comparative analysis of their emphases. For instance, the improved methods of time-escaped algorithm include accelerative time-escaped algorithm, different criterion for convergence time-escaped algorithm and rotation accelerative time-escaped algorithm. Researches the design of images'another characteristic data-color, and discuss existent methods of color design which have been divided into three classes: color design according to iterations, color design according to distance from coloring point to center point and color design according to the value of iterated point.(3)On the basis of visualization processes of general M-J sets, advances the method using genetic algorithm whose gene is images'color to generate and render the images, and achieves a good visualization effect. Studies the evaluation method of images, and gives a fractal images evaluation model based on artificial neural network which use the color psychological effect of user for images as evaluating indicator.(4)Adopts VC++6.0 as development tool, utilizes visualization characteristic data of general M-J sets images(including complex mappings'parameters and color parameters of images) combining with algorithm as main design ides, the general M-J sets images visualization system (fractal images design software)has been designed and realized. The main functions of this software include realizing images generation after selecting parameters, realizing images management and browsing, automatic design module and images evaluation module. This software not only regards as a test platform on which the researchers study and research fractal theories and fractal images, but also acts as an operating platform on which the images designers design fractal artistic images.(5)At the end of this thesis, illuminates the defect of this paper, and introduces the relative problems which need be solved and attended. At last, the development and application of general M-J sets visualization (fractal images generating) has been viewed.The innovations of this paper include some items:①Giving the conceptual description of the general M-J sets visualization.②Improves the general M-J sets visualization algorithm and color design method, and gains some kinds of beautiful images which can represent the structure characteristics of general M-J sets better and be applied to many design fields.③Advances the method using genetic algorithm whose gene is images color to automatic design the images based on the course of general M-J sets images visualization. Examples show that this method can help users to gain favorite images automatically and quickly.④Gives a fractal images evaluation model of color fitness in some fields based on artificial neural network which use the color psychological effect of user for images as evaluating indicator and achieves a famous effect. The main work of this paper has been applied in the project of product packaging and security features innovative design based on fractal technique, and gains a better experiment effect.