// draws sierpinsky gasket fractal

#include <iostream>
#include <cstdlib>
#include <fstream>
#include <cmath>

using std::cout;
using std::endl;
using std::ofstream;

int main() 
{    
   int i;
   double x, y, r;

   // set geometry

   double side_length = 300.0;  // length of triangle side

   double x1 = 20.0;  // x-coordinate of vertex 1
   double y1 = x1;  // y-coordinate of vertex 1

   double x2 = x1 + side_length;  // x coord of vertex 2
   double y2 = y1;      // y coord of vertex 2

   double x3 = x1 + (side_length/2.0);  // x coord of vertex 3
   double y3 = y1 + sqrt(3)*(side_length/2.0);  // y coord of vertex 3


   // setup file io

   ofstream out_file;
   const char out_file_name[] = "sierpin.dat";	// save data in sierpin.dat

   out_file.open(out_file_name); 


   x = 300.;		    // starting point
   y = 30.;

   const int max = 50000;    // number of iterations

   srand((time(0)));         // seed random nmbr generator. srand & time built-in
   
   for(i=1 ; i<=max ; ++i)            	//  draw the gasket 
   {
     r = rand()/(double)RAND_MAX;      // scale random nmbr

      if (r <= 0.3333)
      {
         x = 0.5*(x + x1);
         y = 0.5*(y + y1);
      }
      else if(r > 0.3333 && r <= 0.6666)
      {
         x = 0.5*(x + x2);
         y = 0.5*(y + y2);
      }   
      else 
      {
         x = 0.5*(x + x3);
         y = 0.5*(y + y3);
      }  
      out_file << x << " " << y << endl;
   }
   out_file.close(); // close output file
   std::cout << "data stored in " << out_file_name << std::endl;

   return 0;
}