Study Of Symmetrical Fractal Figure’s Method Based On Chaotic Attractor

The theory of fractal is a new research direction of the geometry-fractal geometry.It wascalled the geometry of nature because of its ability to simulate the natural scenery.In addition tothe characteristics of ordinary art, fractal graphics have self-similarity and unlimited finestructure in general.Samed as the self-similar characteristic performanced in the spatial scale bythe fractal,the chaotic time show the similarity in the time scale.It can be said,INTRINSICChaos and Fractals.Currently,chaotic fractal figures have been widely used inanti-counterfeiting of trademarks,video games and science fiction movie,occupies a uniqueposition in the pattern design.Chaos is a kind of complex physical phenomena existing in the wider world, as is theinherent characteristics of the nonlinear dynamical system. Chaotic attractor is composed ofinfinite number of iterative point which generated by the chaos function iteratively, is a"graphic" description of the chaotic phenomenon. This figure has obvious fractal characteristics,often referred to as the chaos and fractal graph. There is a kind of chaos and fractal graph notonly has the chaotic phenomena, but also has a large number of built-in symmetricphenomenon.The main content of this paper is aimed at symmetrical fractal figure, which mainlyincludes three aspects: PSO is applied to realize rapid optimization of chaotic attractorparameters; proposing rendering scheme based on color control round; graphical parameterscontrol and graphics drawing. First of all, take advantage of the computer’s display function, toachieve symmetrical fractal images in the cycle, the location, size, color parameters controllableso that users can more easily through these controllable parameters to generate various types ofsymmetry Set Graphics. On the basis of the study, this paper puts forward a new solution--rendering scheme based on color control circle, which can make the design of visual effect bysimple change to the gorgeous and in the end to implement a symmetry chaotic fractal graphsimulation system to a particular programming iteration function system.According to the actual implementation process, concrete research content is as follows: (1) the use of the PSO optimized symmetric fractal graph parameter vectorThis study applys PSO to optimize the parameter of chaotic attractor vector, constructs forparametric components in a particular iteration function vector as the particle expressionmethod and PSO of this problem is established. The experimental results show that, PSO canquickly and effectively obtain the optimal solution for the parameter vector, so as to solve thedifficult problem of generating chaotic fractal figure under huge parameter space.(2) determine a rendering schemeIn this paper, combining the characteristics of the chaos fractal graph and using thedunhuang flying figure color combinations as the fundamental key, puts forward a renderingmethod which uses blue, purple, red, yellow color as dominant tone, exhibiting a dream likereally misty and unreal facial diffuse appeal.(3) symmetrical fractal figure parameters controllableStudying the fractal graph generation principle and method process by consulting a largenumber of references. Taking equivalent mappings with group the model p1a1as example,through studying its generation principle, drawing method, rendering scheme,refines thecontrollable parameters. Ordinary users control these parameters through the dialog box togenerate the satisfied symmetrical fractal pattern.(4) Simulation SystemDeveloped a simple system whose overall design regards simple and easy to operate as astarting point, achieves the goal of parameter optimization and drawing and preservation of thesymmetrical fractal graph. Designs more convenient color dialog, user can specify a palette tochoose color to set the main colors of fractal patterns. This provides a convenient tool for laterstudying.The symmetrical fractal graph which is presented in this paper has a refined spatialstructure, various shapes and rich content. It is not only in theory but also become a hot topic inthe application. By using the computer’s display function, symmetrical fractal figure has startedto cause the attention in the field of textile, printing, anti-counterfeit label and so on.