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#!/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]))