基于IFS的Sierpinski三角形的生成及其推广

Generation and Generalization of Sierpinski-Triangle Based on IFS

阐述了基于IFS的Sierpinski三角形分形图形的生成原理,并对其生成技术进行推广。包括两个方面的推广,第一,生成元形状可以为点、线段、三角形、四边形(正方形)、圆,得到的吸引子相同,由此得到吸引子与生成元形状无关的结论。第二,对Sierpinski三角形的IFS进行适当的调节,可以得到新的IFS,并生成新的吸引子,这为从已知的IFS得到新的IFS提供了参考方法。

The technology and algorithm of generating Sierpinski triangle fractal graphics is presented based on IFS,and then it is generalized in two aspects.First,the generator shape can be point,line,triangle,quadrilateral （or square） and circle,but these attractors will be same,so the conclusion is that attractor is independent of generator shape.Second,the IFS with Sierpinski triangle can be modulated to generate new IFS and new attractors,so this is a valuable method to obtain the new IFS from the given IFS.