Refactor sierpinski_triangle.py (#8068)

* 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>

fractals/sierpinski_triangle.py

@@ -1,76 +1,84 @@
-#!/usr/bin/python
+"""
+Author Anurag Kumar | anuragkumarak95@gmail.com | git/anuragkumarak95
 
-"""Author Anurag Kumar | anuragkumarak95@gmail.com | git/anuragkumarak95
+Simple example of fractal generation using recursion.
 
-Simple example of Fractal generation using recursive function.
+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.
 
-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):
+Usage: python sierpinski_triangle.py <int:depth_for_fractal>
-  - turtle
-
-Python:
-  - 2.6
-
-Usage:
-  - $python sierpinski_triangle.py <int:depth_for_fractal>
-
-Credits: This code was written by editing the code from
-https://www.riannetrujillo.com/blog/python-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
 
-PROGNAME = "Sierpinski Triangle"
 
-points = [[-175, -125], [0, 175], [175, -125]]  # size of triangle
+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 get_mid(p1, p2):
+def triangle(
-    return ((p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2)  # find midpoint
+    vertex1: tuple[float, float],
-
+    vertex2: tuple[float, float],
-
+    vertex3: tuple[float, float],
-def triangle(points, depth):
+    depth: int,
-
+) -> None:
+    """
+    Recursively draw the Sierpinski triangle given the vertices of the triangle
+    and the recursion depth
+    """
     my_pen.up()
-    my_pen.goto(points[0][0], points[0][1])
+    my_pen.goto(vertex1[0], vertex1[1])
     my_pen.down()
-    my_pen.goto(points[1][0], points[1][1])
+    my_pen.goto(vertex2[0], vertex2[1])
-    my_pen.goto(points[2][0], points[2][1])
+    my_pen.goto(vertex3[0], vertex3[1])
-    my_pen.goto(points[0][0], points[0][1])
+    my_pen.goto(vertex1[0], vertex1[1])
 
-    if depth > 0:
+    if depth == 0:
-        triangle(
+        return
-            [points[0], get_mid(points[0], points[1]), get_mid(points[0], points[2])],
+
-            depth - 1,
+    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(
+    triangle(vertex3, get_mid(vertex3, vertex2), get_mid(vertex1, vertex3), depth - 1)
-            [points[1], get_mid(points[0], points[1]), get_mid(points[1], points[2])],
-            depth - 1,
-        )
-        triangle(
-            [points[2], get_mid(points[2], points[1]), get_mid(points[0], points[2])],
-            depth - 1,
-        )
 
 
 if __name__ == "__main__":
     if len(sys.argv) != 2:
         raise ValueError(
-            "right format for using this script: "
+            "Correct format for using this script: "
-            "$python fractals.py <int:depth_for_fractal>"
+            "python fractals.py <int:depth_for_fractal>"
         )
     my_pen = turtle.Turtle()
     my_pen.ht()
     my_pen.speed(5)
     my_pen.pencolor("red")
-    triangle(points, int(sys.argv[1]))
+
+    vertices = [(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
+    triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))