Sierpinski triangle

Sierpinski triangle is a fractal and attractive fixed set with the overall shape of an equilateral triangle. It subdivides recursively into smaller triangles. 
 

👁 Sierpinski_triangle1

Examples : 

Input : n = 4
Output :
 * 
 * * 
 * * 
* * * * 

Input : n = 8
Output :
 * 
 * * 
 * * 
 * * * * 
 * * 
 * * * * 
 * * * * 
* * * * * * * * 

 

Approach : 
 

Sierpinski Triangle will be constructed from an equilateral triangle by repeated removal of triangular subsets. 
Steps for Construction : 
1 . Take any equilateral triangle . 
2 . Divide it into 4 smaller congruent triangle and remove the central triangle . 
3 . Repeat step 2 for each of the remaining smaller triangles forever. 

Below is the program to implement Sierpinski triangle 
 

Output : 
 

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

Time complexity: O(n²) 
Auxiliary space: O(1)

References : Wiki