sierpinski_triangle.py

#!/usr/bin/python
# encoding=utf8

'''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 turtle
import sys
PROGNAME = 'Sierpinski Triangle'
if len(sys.argv) !=2: 
    raise Exception('right format for using this script: $python fractals.py <int:depth_for_fractal>')

myPen = turtle.Turtle()
myPen.ht()
myPen.speed(5)
myPen.pencolor('red')

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)


triangle(points,int(sys.argv[1]))