Research On NIFS Architecture And Modeling Method

Fractal phenomena are common in nature,the generation of fractal theory provides a new angle and effective method for people to study the complex phenomena in nature.Iterated function system is the core of fractal theory,it has been a research hotspot in fractal geometry at home and abroad.Its research results have been used to solve many practical problems,such as the simulation of computer natural landscape,medical images,video games,fractal art,and image compression.With the rapid development of computer graphics and the continuous improvement of computer hardware,it makes the strange and colorful fractal graphics appear on the computer.On the construction of fractal graphics,the nonlinear iterated function systems(NIFS)has powerful modeling ability.It is not limited to the compression affine transformation,and can use more nonlinear transformation to design fractal graphics.However,the NIFS architecture is not perfect enough,and the modeling control method of NIFS attractor is not uniform.It can be worth further study.Therefore,in order to draw a lot of fractal graphics with various forms and new shapes,and provide effective method for NIFS modeling control,this topic focuses on the NIFS architecture and NIFS attractor modeling control methods.The main research contents are as follows:First,the research on the architecture and modeling method of NIFS,it mainly includes the composition method of NIFS and the representation of nonlinear transformation,the generation algorithm of NIFS attractor(deterministic algorithm and random iterated algorithm),NIFS modeling method,NIFS rendering method and so on.Secondly,the types of nonlinear transformation provided by fractal flame are limited,this thesis gives one set of nonlinear transformation functions,from which one variate or multivariate functions are chosen to construct the nonlinear transformation of NIFS.This method greatly expands the types of nonlinear transformation of NIFS,and uses easily,which provides an effective method for the construction of nonlinear transformation.Thirdly,for the study of the NIFS modeling control method based on arbitrary nonlinear transformation,this thesis introduces a synthesis method for nonlinear transformation and affine transformation.By adding nonlinear transformations into IFS,we can render NIFS attractor by using the suggested method and the fractal flame method,respectively.Both methods use affine transformation to control the nonlinear transformation.However,the nonlinear transformation controlled by the suggested method is predictable.Experimental results show that the NIFS attractors constructed by two methods can be converted to each other by affine transformation.The suggested method can draw novel and intuitive fractal graphics,and controls easily,which provides an effective way for the construction of NIFS architecture.The results of this thesis have the theoretical guiding significances for the research of NIFS architecture and the interactive design of NIFS fractal graphics.