# 谢尔宾斯基地毯

## 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

1. ^ 创意之窗概念缘起：谢尔宾斯基（Sierpinski）地毯. 创意中国. [2010-02-09]. （原始内容存档于2010-01-03）.