# 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:

 `// C++ code to implement ` `// Sierpinski Triangle using Graphics ` ` `  `#include ` `#include ` `#include ` ` `  `#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; ` `} `

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

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