Add Gosper curve fractal implementation

fractals/gosper_curve.py

@@ -0,0 +1,68 @@
+"""
+A Python implementation of the Gosper curve using the turtle module.
+Reference: https://en.wikipedia.org/wiki/Gosper_curve
+"""
+
+import math
+import turtle
+
+
+def draw_gosper_curve(
+    side_length: float, depth: int, direction: int = -1, angle: float = 60.0
+) -> None:
+    """
+    Recursively draws a Gosper curve fractal.
+
+    Args:
+        side_length: The length of the current segment.
+        depth: The recursive depth of the curve.
+        direction: The direction of the drawing (1 or -1).
+        angle: The angle of the turns in degrees.
+    """
+
+    if depth == 0:
+        turtle.forward(side_length)
+    else:
+        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.penup()
+    turtle.goto(0, -200)
+    turtle.pendown()
+    turtle.speed(0)
+    turtle.width(1)
+
+    draw_gosper_curve(side_length=200.0, depth=4, direction=-1, angle=60.0)
+
+    turtle.exitonclick()