介提出者
谢尔宾斯基地毯是由瓦茨瓦夫·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。
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。如下图
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 caseif (x<1)
{return 0;}
{/*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/3and prepares for recursive callx-=x2*width/3;y-=y2*height/3}return isSierpinskiCarpetPixelFilled(x,y,width/3,height/3);
