Research On Constructing Method Of Super - Complex Generalized J - Set

Mandlebrot once said:"In fact, both from a scientific point of view or from the aestheticpoint of view, when first saw fractal many people can have a new feeling." Natural, complex,elegant, mysterious fractal diagram attracts so many mathematicians, computer scientists, artistsfor their fascinating. Among the large family of fractal, complex iteration fractal can bestrepresent the fractal’s figure nature and characteristics. J sets are typical complex iterativefractals, studied of it’s constructor in some extent represents a fractal map, especially for thewhole idea of the complex iterative fractal.Traditional complex iterative fractal diagram is based on iteration conventional on thecomplex plane, the complex includes an imaginary part and a real part, have two parts. If madethe complex expands more than one imaginary part, the formation of the so-called ternarynumber, quaternions, and we referred such complex to the hyper complex. Fractal graphs whichbased on the hyper complex iterative operation, will involve many new algorithms andtechniques, will produce some new, particularly complex three-dimensional fractal graphs. Thepurpose of this study is constructed to reflect by similarity, since radioactivity, aliquots of thefine structure of the essential characteristics of a three-dimensional shape J set fractal picture.There are many factors affects J set fractals, such as different definition of hyper complex,different drawing methods or different color scheme,they all can affect the J set final formfractals shape and color. In this paper, I studied the definition of hyper complex, the mappingmethod of three-dimensional J set fractal, the color scheme, and the realization of a computersimulation. After a lot of research, experiments, the paper give a preliminary analysis of theexperimental results. Specifically, the research paper mainly involves the following aspects:(1) Definition of hyper complexDifferent definitions of hyper complex have different influence on the final figuregenerated fractal graphs. In this paper, after experimental studies, identified three different tdefinitions of ternary number, relatively speaking, they are re-iterating through the visible areaof the screen is relatively easy to produce with the more obvious characteristics of fractalpattern, different ternary number has relatively large difference on the generate graphical.(2) Drawing process of fractal.Fractal image rendering process includes drawing method, color scheme and participationiteration complex space. Based on the traditional escape radius, to do a certain degree ofimprovement. The escape radius setting is no longer fixed, but can set by their own, and cancombine the drawing method and color scheme. In setting iteration of complex space, this paperbased on the coordinate axes were taken the same amount of division, based on the center of theproliferation of complex point selection method, so to generate a three-dimensional fractal graphs or line with cubes and other shapes.(3) Color schemeFirst, the use of ternary number in excess number to carry the color information. Based onthe color scheme of the regular fractal picture, this is the most intuitive and most likely to thinkof this program. With this "meta" to carry the color factor, in order to get a wide variety ofgraphics, this number’s initial value have different definitions.Second, based on the theme color of the color scheme. The so-called "theme color"consists of several specified color to determine. In rendering three-dimensional J set when thereal part of all three radial mapped to the three-dimensional coordinates. In order to make thetransition between colors is not too obtrusive, we use the "color gradient algorithm" to get a softcolor transitions, J set fractal maps and algorithm selection by the critical mass of uniquedefinition.Third, begin with the primary colors of the color scheme. The so-called color means acolor that is random or specified by the user in a drawing start (iteration take initial value), thenthe iterative process, through the color conversion function, to obtain a second, a third color.This Fu color scheme of color control is very simple, and d ifferent color conversion function, itcan produce different results, and sometimes the effect can be "surprising" in Design andImplementation(4) Simulation SystemBased on the previous studies, this study based on VC++6.0and SQL Server2008software environment developed a simple experimental system. Experimental results show thathyper complex J sets generated basically meet the design requirements.