gistfile1.cpp

#include <cstdlib>
#include <iostream>

using namespace std;

int main(int argc, char *argv[])
{
    /**
* 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 1 of 2
        if ((x <= 0)||(y <= 0)||(x>=width)||(y>=height)) //top row or left column or out of bounds should be full
        {
                return 1;
        }
        {
                /*
                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
 
                // base case 2 of 2
                if (x2 == 1 && y2 == 1) // if in the center square, it should be empty
                        return 0;
 
                // general case
 
                /* offset x and y so it becomes bounded by 0..width/3 and 0..height/3
                and prepares for recursive call
                some offset is added to make sure the parts have all the correct size when
                width and height isn't divisible by 3
                */
                x -= (x2 * width+2)  / 3; 
                y -= (y2 * height+2) / 3;
                width  = (width +2-x2)/3;
                height = (height+2-y2)/3;
        }
 
        return isSierpinskiCarpetPixelFilled(x, y, width, height);
}
    
    system("PAUSE");
    return EXIT_SUCCESS;
}