Add Gosper curve fractal implementation

fractals/gosper_curve.py

@@ -0,0 +1,83 @@
+"""
+Description
+    The Gosper curve (also known as the flowsnake) is a fractal curve discovered
+    by Bill Gosper. It is generated recursively by replacing each line segment
+    with a specific pattern of smaller segments rotated by multiples of
+    60 degrees.
+
+    With each iteration, the curve becomes more complex and gradually fills
+    a hexagonal region.
+
+    (description adapted from https://en.wikipedia.org/wiki/Gosper_curve)
+
+Requirements (pip):
+    - turtle (standard library)
+"""
+
+import math
+import turtle
+
+
+def draw_gosper_curve(
+    side_length: float, depth: int, direction: int = -1, angle: float = 60.0
+) -> None:
+    """
+    Recursively draw a Gosper curve using turtle graphics.
+
+    Args:
+        side_length: Length of the current segment.
+        depth: Recursive depth of the fractal.
+        direction: Direction of the curve (1 or -1).
+        angle: Turn angle in degrees.
+
+    Note:
+        Do not run this as a doctest; it uses turtle graphics.
+    """
+    if depth == 0:
+        turtle.forward(side_length)
+        return
+
+    side_length /= math.sqrt(7)
+    depth -= 1
+
+    if direction == -1:
+        draw_gosper_curve(side_length, depth, -1, angle)
+        turtle.left(angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+        turtle.left(2 * angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+        turtle.right(angle)
+        draw_gosper_curve(side_length, depth, -1, angle)
+        turtle.right(2 * angle)
+        draw_gosper_curve(side_length, depth, -1, angle)
+        draw_gosper_curve(side_length, depth, -1, angle)
+        turtle.right(angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+        turtle.left(angle)
+    else:
+        turtle.right(angle)
+        draw_gosper_curve(side_length, depth, -1, angle)
+        turtle.left(angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+        turtle.left(2 * angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+        turtle.left(angle)
+        draw_gosper_curve(side_length, depth, -1, angle)
+        turtle.right(2 * angle)
+        draw_gosper_curve(side_length, depth, -1, angle)
+        turtle.right(angle)
+        draw_gosper_curve(side_length, depth, 1, angle)
+
+
+if __name__ == "__main__":
+    turtle.title("Gosper Curve")
+    turtle.speed(0)
+
+    turtle.penup()
+    turtle.goto(0, -200)
+    turtle.pendown()
+
+    draw_gosper_curve(200.0, 4)
+
+    turtle.exitonclick()