Research On The Visualization 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. 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.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. 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.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.