On The Algorithm Of Fractal Image Form Complex Dynamic System

Fractal is a science newly developed in the past 20 years, which is a major means in the study on the complicated geometric figures. Graphics design based on the fractal theory of the complex plane can make lines and colors that cannot be worked out by the most gifted artists. Based on a detailed research on several aspects of this marvel, this dissertation made the following achievements:1. The classical Mandelbrot set and Julia set were extended to high order. A new algorithm was presented which can produce a high order Julia set by the random iterate inverse function, and the effect of the iterate times and convergence semi-diameter in graph forming process was discussed.2. According to the connected of the Julia set and the continuity of the color, a divided and conquered graph-forming algorithm was given in the process of forming the artistic graph by making use of Newton-Raphson method.3. A proper improvement to the Newton iterate method was made. Four shaping controlling parameter introduced by converse shape transformation make the graph more flexible and be adjusted by the designer.