On Simulation Of Trees Applying Fractal Geometry

Since 1970 when B. Mandelbrot lodged the fractal concept in the science of geometry, Fractal Geometry ,as a newly emerging overlapping science , has been extensively respected in nonlinear academic circles. Especially in the field of the simulation of the natural scenery, the fractal technique shows its unique advantage and becomes one of the hottest spots for researchers today. Though with all-inclusive features, nature often shows its self-similarity in common. Fractal Geometry, characterizing this kind of feature perfectly, is an important mathematical instrument. With fractal theory, we can not only create different scenes easily but also create vivid hills, terrain, trees etc on the computers which are to the extent of mixing the false with genuine. Fractal methods are of various representations. Rational choices from these forms should meet practical needs.The thesis aims to illustrate the modeling and visualizing of one of the natural scenery —plants, which is one branch of simulation of natural scenery. It first makes an outlining description of present researching achievements on the field .It further studies and probes many key techniques which include custom-made L-system, ramifications and mighty limbs, leaves distribution, etc. A typical method, Iterated Function System (IFS), is demonstrated with details to illustrate the means of drawing fractal picture and the single algorithm of fractal affine transformation ,and taking receiving IFS parameters of a leaf as an example the paper defines the confirmation methods of IFS parameters and summarizes them. On the basis of this , the thesis also puts forward a type of fully parametric IFS combined with L-system and realizes the simulation of trees models on three dimensions. That is to combine the computational graphics with the practical arithmetical technology during the process of simulation to model objects and achieve the expected realization effects. At the same time , it appliesthe modified IFS in which adjusts and controls the parts of the IFS efficiently and offers a deep illustration.The full text makes emphasis of plants simulation , and gives attention to two of modeling some other natural scenes, such as cloud and forest.