系统构造混沌动力系统M-J分形图机制研究

With the rapid advancement of science and technology, lots of intersectional and synthetical subjects are developed by penetrating mutually among different scientific fields. Nonlinear science is a right profound synthetical science,and chaotic dynamics and fractal geometry are important components of nonlinear science. Accompany the great progress of computer technology, these science fields extend from pure sicence fields to application science category. In recent years, the research on chaos and fractal is more and more recognized by the governments and the scholars all over the world, and the research on visual presentation of dynamical system has become one of hotspots in international scientific researches. However, there are many mappings to need to take much time to investigate the mechanism of constructing chaos and fractal images from them. Knowing the mechanism of constructing chaos and fractal images, we can find the key to open the gate of fractal image treasury, and we can use all kinds of methods of constructing fractal images to generate beautiful pictures in batches and can lay the foundation for industrial application of fractal images..Prof. Ning CHEN, the principal of the research subject, has done a great quantity research work on orderly constructing fractal images from complex dynamical system since 1994. She used the complex mapping ( )to construct M-J chaos and fractal images in both C and Z planes, and some new rules and phenomena are discovered and research development was published in the 《Computers and Graphics》(U.S.A.,1998). Because of the previous research work, she obtained the financial aid of China National Natural Science Foundation in 1999-the title of the subject is Research on the Mechanism of Constructing M-J Fractal Images Systematically from Chaotic dynamical Systems (No.69973033). It is related to computer science, mathematics and nonlinear science. During the research of visual presentation of chaotic system by using computer, we want to discover the mechanism of constructing orderly novel chaos and fractal images and intrinsic essence and scientific meaning behind the complex behaviours. With continual endeavor of all members of the subject group in three years, the subject has been completed now. The creative research result have been acquired in theory study, software development and industrialization application research, the papers have been published in the " Computers& Graphics" (2000 Issue 6,2002 Issue 2), "Journal of Computer Research and Development "(2000 Issue 2,2001 Issue 12), " Mini-Micro System "(2001 Issue 12, one article accepted in 2003), "Journal of Shenyang Architecture and Civil Engineering University"(2002 Issue 1,2003 Issue 1) . The research result "Researches on Mechanism of Constructing chaos and fractal Images and Industrial application of chaos and fractal image technology"is awarded the second prize of the Science and Technology Advancing Prize from the government of Liao Ning Province in 2002. The main research results are as follows:.(1) The transcendental mapping " " and Newton's transformation are constructed, the method of VCPS which denotes valid critical point set is presented to construct generated M sets of analytical mapping with countable infinite critical points . The subject advanced the approach of "period link" and generated quantities of fill-in J sets;(2) According to the notion of limit image of "Escher"，chaos and fractal images in upper half-plane、orbicular limit and square limit are constructed;(3) With the construction of generalized Mandelbrot sets from un-analytic module group equivalent mappings and the definition of "symmetric arrangement for color", the fill-in J sets are generated;(4) According to mathematic properties of visual presentation of planar group with D4 symmetry, corresponding generalized M sets and generalized fill-in J sets are constructed, which set up a good foundation for further research on visual presentation of planar tiling mappings;.(5) A chaos and fractal software convenient to

本项目具有计算机科学、数学科学及非线性科学等多学科交叉特征，是非线性科学中复杂系统研究热点。研究构造混沌动力系统新颖分形图机制，找出M-J分形图拓扑不变规律，揭示丛有形谠诒局始捌淇蒲诤⑾中孪窒螅岢鲂滤惴ǎ谙低秤行蚬乖旎煦绶中瓮蓟蒲芯糠矫娲锏焦柿煜人健Ｎ中瓮嫉南低彻乖旌陀τ锰峁├砺垡谰荨?..