Python/fractals/sierpinski_triangle.py

"""
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]))
    turtle.Screen().exitonclick()