Variant of the Sierpinski curves in C++; help

[John O' Meara]

using namespace std;

enum direction {north, east, south, west };

direction right(direction d)
{ // return the direction to the right (clockwise)
  switch(d) {
    case north:  return east;
    case east:   return south;
    case south: return west;
    case west:  return north;
   }
}

ostream& operator<<(ostream& c, direction d)
{ // write a direction
  switch(d) {
    case north:   c << "north"; break;
    case east:     c << " east"; break;
    case south:   c << "south"; break;
    case west:    c << " west"; break;
   }
}

void edge(direction d, int i);
direction left(direction d);

void Sierpinski(int i)
{ // Draw Sierpinski curve of order i
  direction d = north;
  do {
    edge(d, i);
    d = right(d);
  }while(d != north);
}

direction left(direction d, int i)
{ // Return direction to the left (counterclockwise)
  switch(d) {
    case north:    return west;
    case east:     return north;
    case south:   return east;
    case west:    return south;
   }
}

void edge(direction d, int i)
{
   if(i == -1)
       cout << d << " 2 cm\n";
   else {
       edge(left(d), i-1);
       edge(d, i-1);
       edge(right(d), i-1);
   }
}

int main()
{
   Sierpinski(1);

   return 0;
}

The question is question 3 in the attachment. The program above for a first order curve Sierpinski(1); it "draws" a zero order curve and then overwirtes that cross shape three times. I cannot get it to draw the first order or higher order curves. Because the only other symmetry I can see in the zero order curve is central symmetry in the center of the cross. I don't know how to break the zero order curve down to simplier components, than north, south, east and west directions? Looking at the attachment is the only way you are going to know what I am talking about, there are drawings of zero, first, second and third order curves. Thanks for the help in advance.

 

[Valkarie]

Sorry for the long question. ![enter image description here][1] [1]: https://i.stack.imgur.com/W5aXF.png</code>I am trying to make a program that will draw a Sierpinski curve of any order. The program I have written can only draw the zero order curve. Here is my code. A:The Sierpinski curve is defined by a simple recursive formula. You can look at it like this:A 0th order curve is just a straight line.A 1st order curve is made up of 3 0th order curves, arranged in an "L" shape.A 2nd order curve is made up of 3 1st order curves, arranged in an "L" shape.A 3rd order curve is made up of 3 2nd order curves, arranged in an "L" shape.etc.So, all you need to do is keep track of what order you're drawing, and draw the appropriate number of lower-order curves in the right orientation.