Sierpinski Triangle using Graphics

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

Approach:



  • In the given segment of codes, a triangle is made and then draws out three other adjacent small triangles till the terminating condition which checks out whether the height of the triangle is less than 5 pixels returns true.
  • We only need to verify whether a given triangle is smaller than 5 pixels since beyond that the triangles would start converging at fixed points.
  • A counter colorVal is defined for in response to the aesthetic need of the triangle and in all, it cycles through all the available colours by iterating every triangle set.
  • Using this methodology we can also further implement a fractal zoom and hypothetically provide an infinite zoom later.

Below is the implementation of the above approach:

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ code to implement
// Sierpinski Triangle using Graphics
  
#include <math.h>
#include <stdlib.h>
#include <winbgim.h>
  
#define Y 900
#define X 1600
  
// Defining a function to draw a triangle
// with thickness 'delta'
void triangle(float x, float y,
              float h, int colorVal)
{
    setcolor(colorVal % 15 + 1);
  
    for (float delta = 0; delta > -5; delta -= 1) {
        line(x - (h + delta) / sqrt(3),
             y - (h + delta) / 3,
             x + (h + delta) / sqrt(3),
             y - (h + delta) / 3);
        line(x - (h + delta) / sqrt(3),
             y - (h + delta) / 3,
             x,
             y + 2 * (h + delta) / 3);
        line(x,
             y + 2 * (h + delta) / 3,
             x + (h + delta) / sqrt(3),
             y - (h + delta) / 3);
    }
}
  
// Defining a function to draw
// an inverted triangle
// with thickness 'delta'
void trianglev2(float x, float y,
                float h, int colorVal)
{
    setcolor(colorVal % 15 + 1);
  
    for (float delta = 0; delta > -1 + 5; delta -= 1) {
  
        line(x - (h + delta) / sqrt(3),
             y + (h + delta) / 3,
             x + (h + delta) / sqrt(3),
             y + (h + delta) / 3);
        line(x - (h + delta) / sqrt(3),
             y + (h + delta) / 3,
             x,
             y - 2 * (h + delta) / 3);
        line(x,
             y - 2 * (h + delta) / 3,
             x + (h + delta) / sqrt(3),
             y + (h + delta) / 3);
    }
}
  
// A recursive function to draw out
// three adjacent smaller triangles
// while the height is greater than 5 pixels.
int drawTriangles(float x = X / 2,
                  float y = 2 * Y / 3,
                  float h = Y / 2,
                  int colorVal = 0)
{
  
    if (h < 5) {
        return 0;
    }
  
    if (x > 0 && y > 0 && x < X && y < Y) {
        triangle(x, y, h, colorVal);
    }
  
    drawTriangles(x,
                  y - 2 * h / 3,
                  h / 2,
                  colorVal + 1);
    drawTriangles(x - h / sqrt(3),
                  y + h / 3,
                  h / 2,
                  colorVal + 1);
    drawTriangles(x + h / sqrt(3),
                  y + h / 3,
                  h / 2,
                  colorVal + 1);
  
    return 0;
}
  
// Driver code
int main()
{
    initwindow(X, Y);
    trianglev2(X / 2, 2 * Y / 3, Y, 2);
  
    drawTriangles();
    getch();
    closegraph();
  
    return 0;
}

chevron_right


Output:



My Personal Notes arrow_drop_up

Strangely attracted towards the beautiful world of graphical programming Fractals are the most aesthetic objects in this universe

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.