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
Credits: This code was written by editing the code from http://www.lpb-riannetrujillo.com/blog/python-fractal/
'''
import sys
import turtle
PROGNAME = 'Sierpinski Triangle'
if len(sys.argv) != 2:
raise Exception('right format for using this script: $python fractals.py ')
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]))