mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
9f041e9cc8
* updating DIRECTORY.md
* Update sierpinski_triangle.py header doc
* Remove unused PROGNAME var in sierpinski_triangle.py
The PROGNAME var was used to print an image description in the reference
code that this implementation was taken from, but it's entirely unused
here
* Refactor triangle() function to not use list of vertices
Since the number of vertices is always fixed at 3, there's no need to
pass in the vertices as a list, and it's clearer to give the vertices
distinct names rather than index them from the list
* Refactor sierpinski_triangle.py to use tuples
Tuples make more sense than lists for storing coordinate pairs
* Flip if-statement condition in sierpinski_triangle.py to avoid nesting
* Add type hints to sierpinski_triangle.py
* Add doctests to sierpinski_triangle.py
* Fix return types in doctests
* Update fractals/sierpinski_triangle.py
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
85 lines
2.6 KiB
Python
85 lines
2.6 KiB
Python
"""
|
|
Author Anurag Kumar | anuragkumarak95@gmail.com | git/anuragkumarak95
|
|
|
|
Simple example of fractal generation using recursion.
|
|
|
|
What is the Sierpiński Triangle?
|
|
The Sierpiński triangle (sometimes spelled Sierpinski), also called the
|
|
Sierpiński gasket or Sierpiński sieve, is a fractal 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—that is, it is a mathematically
|
|
generated pattern that is reproducible at any magnification or reduction. It is
|
|
named after the Polish mathematician Wacław Sierpiński, but appeared as a
|
|
decorative pattern many centuries before the work of Sierpiński.
|
|
|
|
|
|
Usage: python sierpinski_triangle.py <int:depth_for_fractal>
|
|
|
|
Credits:
|
|
The above description is taken from
|
|
https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle
|
|
This code was written by editing the code from
|
|
https://www.riannetrujillo.com/blog/python-fractal/
|
|
"""
|
|
import sys
|
|
import turtle
|
|
|
|
|
|
def get_mid(p1: tuple[float, float], p2: tuple[float, float]) -> tuple[float, float]:
|
|
"""
|
|
Find the midpoint of two points
|
|
|
|
>>> get_mid((0, 0), (2, 2))
|
|
(1.0, 1.0)
|
|
>>> get_mid((-3, -3), (3, 3))
|
|
(0.0, 0.0)
|
|
>>> get_mid((1, 0), (3, 2))
|
|
(2.0, 1.0)
|
|
>>> get_mid((0, 0), (1, 1))
|
|
(0.5, 0.5)
|
|
>>> get_mid((0, 0), (0, 0))
|
|
(0.0, 0.0)
|
|
"""
|
|
return (p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2
|
|
|
|
|
|
def triangle(
|
|
vertex1: tuple[float, float],
|
|
vertex2: tuple[float, float],
|
|
vertex3: tuple[float, float],
|
|
depth: int,
|
|
) -> None:
|
|
"""
|
|
Recursively draw the Sierpinski triangle given the vertices of the triangle
|
|
and the recursion depth
|
|
"""
|
|
my_pen.up()
|
|
my_pen.goto(vertex1[0], vertex1[1])
|
|
my_pen.down()
|
|
my_pen.goto(vertex2[0], vertex2[1])
|
|
my_pen.goto(vertex3[0], vertex3[1])
|
|
my_pen.goto(vertex1[0], vertex1[1])
|
|
|
|
if depth == 0:
|
|
return
|
|
|
|
triangle(vertex1, get_mid(vertex1, vertex2), get_mid(vertex1, vertex3), depth - 1)
|
|
triangle(vertex2, get_mid(vertex1, vertex2), get_mid(vertex2, vertex3), depth - 1)
|
|
triangle(vertex3, get_mid(vertex3, vertex2), get_mid(vertex1, vertex3), depth - 1)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
if len(sys.argv) != 2:
|
|
raise ValueError(
|
|
"Correct format for using this script: "
|
|
"python fractals.py <int:depth_for_fractal>"
|
|
)
|
|
my_pen = turtle.Turtle()
|
|
my_pen.ht()
|
|
my_pen.speed(5)
|
|
my_pen.pencolor("red")
|
|
|
|
vertices = [(-175, -125), (0, 175), (175, -125)] # vertices of triangle
|
|
triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))
|