Task
Produce an ASCII representation of a Sierpinski triangle of order   N.



Example
The Sierpinski triangle of order   4   should look like this:

                       *
                      * *
                     *   *
                    * * * *
                   *       *
                  * *     * *
                 *   *   *   *
                * * * * * * * *
               *               *
              * *             * *
             *   *           *   *
            * * * *         * * * *
           *       *       *       *
          * *     * *     * *     * *
         *   *   *   *   *   *   *   *
        * * * * * * * * * * * * * * * *



Related tasks
 Sierpinski triangle/Graphical for graphics images of this pattern. 
 Sierpinski carpet


#include <iostream>
#include <string>
#include <list>
#include <algorithm>
#include <iterator>
 
using namespace std;
 
template<typename OutIt>
void sierpinski(int n, OutIt result)
{
    if( n == 0 )
    {
        *result++ = "*";
    }
    else
    {
        list<string> prev;
        sierpinski(n-1, back_inserter(prev));
 
        string sp(1 << (n-1), ' ');
        result = transform(prev.begin(), prev.end(),
            result,
            [sp](const string& x) { return sp + x + sp; });
        transform(prev.begin(), prev.end(),
            result,
            [sp](const string& x) { return x + " " + x; });
    }
}
 
int main()
{
    sierpinski(4, ostream_iterator<string>(cout, "\n"));
    return 0;
}