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. Examples :

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

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

C++

 // C++ program to print sierpinski triangle. #include using namespace std;    void printSierpinski(int n) {     for (int y = n - 1; y >= 0; y--) {            // printing space till         // the value of y         for (int i = 0; i < y; i++) {             cout<<" ";         }            // printing '*'         for (int x = 0; x + y < n; x++) {            // printing '*' at the appropriate position         // is done by the and value of x and y         // wherever value is 0 we have printed '*'         if(x & y)             cout<<" "<<" ";         else             cout<<"* ";         }            cout<

Java

 // Java program to print  // sierpinski triangle. import java.util.*; import java.io.*;    class GFG  {     static void printSierpinski(int n)     {         for (int y = n - 1; y >= 0; y--) {                // printing space till             // the value of y             for (int i = 0; i < y; i++) {                 System.out.print(" ");             }                // printing '*'             for (int x = 0; x + y < n; x++) {                    // printing '*' at the appropriate                 // position is done by the and                  // value of x and y wherever value                 // is 0 we have printed '*'                 if ((x & y) != 0)                     System.out.print(" "                                     + " ");                 else                     System.out.print("* ");             }                System.out.print("\n");         }     }        // Driver code     public static void main(String args[])     {         int n = 16;            // Function calling         printSierpinski(n);     } }    // This code is contributed by Sahil_Bansall

Python3

 # Python 3 program to print  # sierpinski triangle.    def printSierpinski( n) :            y = n - 1     while(y >= 0) :                    # printing space till         # the value of y         i = 0         while(i < y ):             print(" ",end="")             i = i + 1            # printing '*'         x = 0         while(x + y < n ):                # printing '*' at the appropriate             # position is done by the and              # value of x and y wherever value             # is 0 we have printed '*'             if ((x & y) != 0) :                 print(" ", end = " ")             else :                 print("* ", end = "")             x =x + 1                    print()         y = y - 1            # Driver code n = 16    # Function calling printSierpinski(n)       # This code is contributed by Nikita Tiwari.

C#

 // C# program to print // sierpinski triangle. using System;    class GFG {     static void printSierpinski(int n)     {         for (int y = n - 1; y >= 0; y--) {                // printing space till             // the value of y             for (int i = 0; i < y; i++) {                 Console.Write(" ");             }                // printing '*'             for (int x = 0; x + y < n; x++) {                    // printing '*' at the appropriate                 // position is done by the and                 // value of x and y wherever value                 // is 0 we have printed '*'                 if ((x & y) != 0)                     Console.Write(" " + " ");                 else                     Console.Write("* ");             }                Console.WriteLine();         }     }        // Driver code     public static void Main()     {         int n = 16;            // Function calling         printSierpinski(n);     } }    // This code is contributed by vt_m

PHP

 = 0; \$y--)      {            // printing space till         // the value of y         for (\$i = 0; \$i < \$y; \$i++)         {             echo " ";         }            // printing '*'         for (\$x = 0; \$x + \$y < \$n; \$x++)          {            // printing '*' at the appropriate          // position is done by the and value          // of x and y wherever value is 0 we          // have printed '*'         if(\$x & \$y)             echo"  ";         else             echo"* ";         }            echo "\n";     } }    // Driver code \$n = 16; printSierpinski(\$n);    // This code is contributed by Mithun Kumar ?>

Output :

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

References : Wiki

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