sierpinski_triangle.py

#!/usr/bin/python

"""Author Anurag Kumar | anuragkumarak95@gmail.com | git/anuragkumarak95

Simple example of Fractal generation using recursive function.

What is Sierpinski Triangle?
>>The Sierpinski triangle (also with the original orthography Sierpinski), also called
the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set
with the overall shape of an equilateral triangle, subdivided recursively into smaller
equilateral triangles. Originally constructed as a curve, this is one of the basic
examples of self-similar sets, i.e., it is a mathematically generated pattern that can
be reproducible at any magnification or reduction. It is named after the Polish
mathematician Wacław Sierpinski, but appeared as a decorative pattern many centuries
prior to the work of Sierpinski.

Requirements(pip):
  - turtle

Python:
  - 2.6

Usage:
  - $python sierpinski_triangle.py <int:depth_for_fractal>

Credits: This code was written by editing the code from
http://www.riannetrujillo.com/blog/python-fractal/

"""
import sys
import turtle

PROGNAME = "Sierpinski Triangle"

points = [[-175, -125], [0, 175], [175, -125]]  # size of triangle


def getMid(p1, p2):
    return ((p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2)  # find midpoint


def triangle(points, depth):

    myPen.up()
    myPen.goto(points[0][0], points[0][1])
    myPen.down()
    myPen.goto(points[1][0], points[1][1])
    myPen.goto(points[2][0], points[2][1])
    myPen.goto(points[0][0], points[0][1])

    if depth > 0:
        triangle(
            [points[0], getMid(points[0], points[1]), getMid(points[0], points[2])],
            depth - 1,
        )
        triangle(
            [points[1], getMid(points[0], points[1]), getMid(points[1], points[2])],
            depth - 1,
        )
        triangle(
            [points[2], getMid(points[2], points[1]), getMid(points[0], points[2])],
            depth - 1,
        )


if __name__ == "__main__":
    if len(sys.argv) != 2:
        raise ValueError(
            "right format for using this script: "
            "$python fractals.py <int:depth_for_fractal>"
        )
    myPen = turtle.Turtle()
    myPen.ht()
    myPen.speed(5)
    myPen.pencolor("red")
    triangle(points, int(sys.argv[1]))