4. A Fractal Pattern

IN C++ Examine this pattern of asterisks and blanks, and write a recursive function that can generate patterns such as this:

*

* * 

 *

* * * *

 *

 * *

 *

* * * * * * * *

 *

 * *

 *

 * * * *

 *

 * *

 *

With recursive thinking, the function needs only seven or eight lines of code (including two recursive calls). Your prototype should look like this:

 void pattern(ostream& outs, unsigned int n, unsigned int i);

 // Precondition: n is a power of 2 greater than zero.

 // Postcondition: A pattern based on the above example has been

 // printed to the ostream outs. The longest line of the pattern has

 // n stars beginning in column i of the output. For example,

 // The above pattern is produced by the call pattern(cout, 8, 0).

Hints: You do not need to check the precondition. Think about how the pattern is a fractal. Can you find two smaller versions of the pattern within the large pattern? Here is some code that may be useful within your function:

 // A loop to print exactly i spaces:

 for (k = 0; k < i; k++) outs << ' ';

 // A loop to print n asterisks, each one followed by a space:

 for (k = 0; k < n; k++) outs << "* ";