基于迭代函数系统的分形植物模拟  

Simulation of Fractal Plant Based on Iteration Function System

作　　者：李彩云 郑红婵[1] 林增耀 

机构地区：[1]西北工业大学理学院,陕西西安

出　　处：《应用数学进展》2018年第1期128-138,共11页Advances in Applied Mathematics

基　　金：陕西省自然科学基础研究计划项目(2016JM6056)。

摘　　要：本文在介绍迭代函数系统(IFS)基本理论的基础上,根据IFS码对给定图像的第一次应用来揭示内部的仿射变换收缩特性,分析了仿射变换个数以及参数对生成分形树的影响,从而修改IFS码,生成了具有不同形态的分形树。利用拟仿射变换实现吸引子图像的插值,并生成三角枫叶、五角枫叶等,通过调整插值点生成形状可控的分形树叶。最后,结合Matlab给出分形图的若干实例。In this paper, based on the introduction of the basic theory of Iterative Function System(IFS), the first application of IFS code to a given image can reveal the shrinkage characteristics of internal affine transformation. The influence of the numbers and parameters of affine transformations on the generation of fractal tree is analyzed. Thus it can generate fractal trees with different mor-phologies by modifying the IFS code. Using pseudo-affine transformation to achieve the interpola-tion of the attractor image, the triangular maple leaves and the pentagon maple leaves are gener-ated. Meanwhile, controllable fractal leaves can be obtained through adjusting interpolation points. Finally, some examples of fractal images are given with Matlab.

关 键 词：分形 景物模拟 拟仿射变换 枫叶 

分 类 号：TP39[自动化与计算机技术—计算机应用技术]