Ulam Spiral written to PNG

ulam_spiral.cpp

/**
* Ulam Spiral
* http://en.wikipedia.org/wiki/Ulam_spiral
* @author Beren Oguz
* @copyright 2015, Beren Oguz
* @license This code is licensed with BSD-2 clause License
* Please see: http://opensource.org/licenses/BSD-2-Clause
*/ 
#include <cstdint>
#include <cmath>

#include <png++/png.hpp>

static constexpr const char* file_name = "ulam-spiral.png";
static constexpr std::size_t image_width = 500;
static constexpr std::size_t image_height =500;

typedef std::uintmax_t Natural;

bool is_prime(Natural num)
{
    if(num==0 || num==1)
    {
        return false;
    }
    else if(num==2 || num==3)
    {
        return true;
    }
    Natural root = std::sqrt(num);
    for(Natural x=2; x<=root; x++)
    {
        if(num%x == 0)
        {
            return false;
        }
    }
    return true;
}

int main()
{
     png::image<png::rgb_pixel> image(image_width, image_height);
     Natural size = 1;
     Natural current = 1;
     bool count = 1;
     Natural nums=1;
     char direction = 0;
     for(std::size_t y = image_height/2; nums < image_height*image_width;)
     {
         for(std::size_t x = image_width/2; nums < image_height*image_width;)
         {
             if(is_prime(nums))
             {
                 image[x][y] = png::rgb_pixel(0,0,0);
             }
             else
             {
                 image[x][y] = png::rgb_pixel(255,255,255);
             }

             nums++;
             current--;
             if(current == 0)
             {
                 if(count)
                 {
                     count = false;
                     current = size;
                 }
                 else
                 {
                     count = true;
                     current = size;
                     size++;
                 }
                 if(direction!=3)
                 {
                     direction++;
                 }
                 else
                 {
                     direction = 0;
                 }
             }
             switch(direction)
             {
                 case 0:
                    x++;
                    break;
                 case 1:
                    y--;
                    break;
                 case 2:
                    x--;
                    break;
                 case 3:
                    y++;
                    break;
             }
         }
     }
     image.write(file_name);
}