add vicsek to fractals (#11306)

Co-authored-by: BastosLaG <bastien.capiaux@gmail.com>

fractals/vicsek.py

@@ -0,0 +1,76 @@
+"""Authors Bastien Capiaux & Mehdi Oudghiri
+
+The Vicsek fractal algorithm is a recursive algorithm that creates a
+pattern known as the Vicsek fractal or the Vicsek square.
+It is based on the concept of self-similarity, where the pattern at each
+level of recursion resembles the overall pattern.
+The algorithm involves dividing a square into 9 equal smaller squares,
+removing the center square, and then repeating this process on the remaining 8 squares.
+This results in a pattern that exhibits self-similarity and has a
+square-shaped outline with smaller squares within it.
+
+Source: https://en.wikipedia.org/wiki/Vicsek_fractal
+"""
+
+import turtle
+
+
+def draw_cross(x: float, y: float, length: float):
+    """
+    Draw a cross at the specified position and with the specified length.
+    """
+    turtle.up()
+    turtle.goto(x - length / 2, y - length / 6)
+    turtle.down()
+    turtle.seth(0)
+    turtle.begin_fill()
+    for _ in range(4):
+        turtle.fd(length / 3)
+        turtle.right(90)
+        turtle.fd(length / 3)
+        turtle.left(90)
+        turtle.fd(length / 3)
+        turtle.left(90)
+    turtle.end_fill()
+
+
+def draw_fractal_recursive(x: float, y: float, length: float, depth: float):
+    """
+    Recursively draw the Vicsek fractal at the specified position, with the
+    specified length and depth.
+    """
+    if depth == 0:
+        draw_cross(x, y, length)
+        return
+
+    draw_fractal_recursive(x, y, length / 3, depth - 1)
+    draw_fractal_recursive(x + length / 3, y, length / 3, depth - 1)
+    draw_fractal_recursive(x - length / 3, y, length / 3, depth - 1)
+    draw_fractal_recursive(x, y + length / 3, length / 3, depth - 1)
+    draw_fractal_recursive(x, y - length / 3, length / 3, depth - 1)
+
+
+def set_color(rgb: str):
+    turtle.color(rgb)
+
+
+def draw_vicsek_fractal(x: float, y: float, length: float, depth: float, color="blue"):
+    """
+    Draw the Vicsek fractal at the specified position, with the specified
+    length and depth.
+    """
+    turtle.speed(0)
+    turtle.hideturtle()
+    set_color(color)
+    draw_fractal_recursive(x, y, length, depth)
+    turtle.Screen().update()
+
+
+def main():
+    draw_vicsek_fractal(0, 0, 800, 4)
+
+    turtle.done()
+
+
+if __name__ == "__main__":
+    main()