sierpinski triangle Algorithm
The Sierpinski triangle (also with the original orthography Sierpiński), also named the Sierpinski gasket or Sierpinski sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. It is named after the Polish mathematician Wacław Sierpiński, but looked as a decorative shape many centuries before the work of Sierpiński.
However, like shapes look already in the 13th-century Cosmati Mosaics in the cathedral of Anagni, Italy, and other places of central Italy, for carpets in many places such as the nave of the Roman Basilica of Santa Maria in Cosmedin, and for isolated triangles placed in rotae in several churches and basilicas. The Apollonian gasket was first described by Apollonius of Perga (3rd century BC) and further analyzed by Gottfried Leibniz (17th century), and is a curved precursor of the 20th-century Sierpiński triangle. Wacław Sierpiński described the Sierpinski triangle in 1915.
#!/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:
- $python sierpinski_triangle.py <int:depth_for_fractal>
Credits: This code was written by editing the code from
http://www.riannetrujillo.com/blog/python-fractal/
"""
import turtle
import sys
PROGNAME = "Sierpinski Triangle"
points = [[-175, -125], [0, 175], [175, -125]] # size of triangle
def getMid(p1, p2):
return ((p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2) # find midpoint
def triangle(points, depth):
myPen.up()
myPen.goto(points[0][0], points[0][1])
myPen.down()
myPen.goto(points[1][0], points[1][1])
myPen.goto(points[2][0], points[2][1])
myPen.goto(points[0][0], points[0][1])
if depth > 0:
triangle(
[points[0], getMid(points[0], points[1]), getMid(points[0], points[2])],
depth - 1,
)
triangle(
[points[1], getMid(points[0], points[1]), getMid(points[1], points[2])],
depth - 1,
)
triangle(
[points[2], getMid(points[2], points[1]), getMid(points[0], points[2])],
depth - 1,
)
if __name__ == "__main__":
if len(sys.argv) != 2:
raise ValueError(
"right format for using this script: "
"$python fractals.py <int:depth_for_fractal>"
)
myPen = turtle.Turtle()
myPen.ht()
myPen.speed(5)
myPen.pencolor("red")
triangle(points, int(sys.argv[1]))
