Complex Dynamic System Of Spatial Fractal Julia Sets

Julia set is important part of the nonlinear theory, and is also a common topic in both chaos and fractals. As an important set in fractals, Julia set clearly shows the character of chaos. It is the most important case to show there is a close relationship between chaos and fractals. In current research of nonlinear theory, spatial-temporal chaos and spatial chaos have been developed and completed, but there is nothing about spatial Julia set. In this case, the researchers focus on how to create spatial Julia set relating spatial-temporal chaos and spatial chaos. In this thesis, we will discuss chaos and fractals, and the method to create the spatial Julia set. The content is as follows:I. The control theory and method of Julia set.In this section, we present the model of the zooming, extending and circumgyrating for Julia set, and give the common model for all of the above, which is the supplement for traditional Julia set.II. Several methods of forming spatial Julia set currently and itsimprovement.In this section, we list three kinds of accepted method to extend Julia set to space, and point out its advantages and disadvantages. Then we improve it by using the method of controlling Julia set, making it more flexible and free.III. Create spatial Julia set based on CML.CML is an important model for researching spatial-temporal chaos. In this part, we discuss the possibility of creating spatial chaos based on CML, and then approve its characters. Finally, we analysis the characters of a certain CML, and plot the spatial Julia set. Then we point out that it is a clear fractal figure.IV. Create spatial Julia set based on spatial chaos.Nowadays, spatial chaos is a new theory in nonlinear fields and how to createspatial Julia set based on spatial chaos is still a blank. In this part, we will introduce the spatial chaos, and analysis the possibility of creating spatial chaos based on it, and then show that it is an extension about traditional Julia set.Finally, we point out the insufficiency about this thesis, propose some problems that need to be solved further and prospect the development of spatial Julia set.