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#!/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]))

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