# 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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