谢尔宾斯基地毯
谢尔宾斯基地毯(、波蘭語:),是由波蘭數學家瓦茨瓦夫·谢尔宾斯基()于1916年提出的一种分形,是自相似集的一种。它的豪斯多夫维是 log 8/log 3 ≈ 1.8928。门格海绵是它在三维空间中的推广。
![](../I/Sierpinski_carpet_5.svg.png.webp)
构造
谢尔宾斯基地毯的构造与谢尔宾斯基三角形相似,区别仅在于谢尔宾斯基地毯是以正方形而非等边三角形为基础的。将一个实心正方形划分为的9个小正方形,去掉中间的小正方形,再对余下的小正方形重复这一操作便能得到谢尔宾斯基地毯。[1]
谢尔宾斯基地毯可以由以下计算机程序构造:
/** Decides if a point at a specific location is filled or not. @param x is the x coordinate of the point being checked @param y is the y coordinate of the point being checked @param width is the width of the Sierpinski Carpet being checked @param height is the height of the Sierpinski Carpet being checked @return 1 if it is to be filled or 0 if it is not */ int isSierpinskiCarpetPixelFilled(int x,int y,int width,int height) { // base case if (x<1) { return 0; } // general case { /* If the grid was split in 9 parts, what part(x2,y2) would x,y fit into? */ int x2 = x*3/width; // an integer from 0..2 inclusive int y2 = y*3/height; // an integer from 0..2 inclusive if (x2==1 && y2==1) // if in the centre squaure, it should be filled. return 1; /* offset x and y so it becomes bounded by 0..width/3 and 0..height/3 and prepares for recursive call */ x-=x2*width/3; y-=y2*height/3; } return isSierpinskiCarpetPixelFilled(x,y,width/3,height/3); }
参考
- . 创意中国. [2010-02-09]. (原始内容存档于2010-01-03).
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.