From 770d9ce7e58329d17d4c4a7069f5097893de329f Mon Sep 17 00:00:00 2001
From: Simon Waldherr <git@simon.waldherr.eu>
Date: Thu, 24 Oct 2024 20:45:58 +0200
Subject: [PATCH 1/3] add Barnsley Fern

---
 fractals/barnsley_farn.py | 53 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 fractals/barnsley_farn.py

diff --git a/fractals/barnsley_farn.py b/fractals/barnsley_farn.py
new file mode 100644
index 000000000000..39db8c5e9bc8
--- /dev/null
+++ b/fractals/barnsley_farn.py
@@ -0,0 +1,53 @@
+"""
+Barnsley Fern
+
+The Barnsley fern is a fractal that uses an iterated function system (IFS) 
+to generate a realistic-looking fern shape.
+
+Reference:
+https://en.wikipedia.org/wiki/Barnsley_fern
+
+Requirements:
+    - matplotlib
+    - numpy
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def barnsley_farn(n_points=100000):
+    """
+    Generates the points of the Barnsley fern.
+    """
+    x, y = 0, 0
+    points = np.zeros((n_points, 2))
+
+    for i in range(n_points):
+        r = np.random.random()
+        if r < 0.01:
+            x, y = 0, 0.16 * y
+        elif r < 0.86:
+            x, y = 0.85 * x + 0.04 * y, -0.04 * x + 0.85 * y + 1.6
+        elif r < 0.93:
+            x, y = 0.2 * x - 0.26 * y, 0.23 * x + 0.22 * y + 1.6
+        else:
+            x, y = -0.15 * x + 0.28 * y, 0.26 * x + 0.24 * y + 0.44
+        points[i] = [x, y]
+
+    return points
+
+
+def plot_barnsley_farn(points):
+    """
+    Plots the Barnsley fern using matplotlib.
+    """
+    x, y = points[:, 0], points[:, 1]
+    plt.scatter(x, y, s=0.1, color='green')
+    plt.title("Barnsley Fern")
+    plt.show()
+
+
+if __name__ == "__main__":
+    fern_points = barnsley_farn()
+    plot_barnsley_farn(fern_points)

From 15bf85ecbf95b469a305edc9b27a4f76a514cecc Mon Sep 17 00:00:00 2001
From: Simon Waldherr <git@simon.waldherr.eu>
Date: Thu, 24 Oct 2024 21:43:50 +0200
Subject: [PATCH 2/3] apply coding style

---
 fractals/barnsley_farn.py | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/fractals/barnsley_farn.py b/fractals/barnsley_farn.py
index 39db8c5e9bc8..d2666157a2a6 100644
--- a/fractals/barnsley_farn.py
+++ b/fractals/barnsley_farn.py
@@ -1,7 +1,7 @@
 """
 Barnsley Fern
 
-The Barnsley fern is a fractal that uses an iterated function system (IFS) 
+The Barnsley fern is a fractal that uses an iterated function system (IFS)
 to generate a realistic-looking fern shape.
 
 Reference:
@@ -12,8 +12,8 @@
     - numpy
 """
 
-import numpy as np
 import matplotlib.pyplot as plt
+import numpy as np
 
 
 def barnsley_farn(n_points=100000):
@@ -23,8 +23,10 @@ def barnsley_farn(n_points=100000):
     x, y = 0, 0
     points = np.zeros((n_points, 2))
 
+    rng = np.random.default_rng()
+
     for i in range(n_points):
-        r = np.random.random()
+        r = rng.random()
         if r < 0.01:
             x, y = 0, 0.16 * y
         elif r < 0.86:
@@ -43,7 +45,7 @@ def plot_barnsley_farn(points):
     Plots the Barnsley fern using matplotlib.
     """
     x, y = points[:, 0], points[:, 1]
-    plt.scatter(x, y, s=0.1, color='green')
+    plt.scatter(x, y, s=0.1, color="green")
     plt.title("Barnsley Fern")
     plt.show()
 

From b079fea0b92d85b88800345765eb1d33b72520dd Mon Sep 17 00:00:00 2001
From: Simon Waldherr <git@simon.waldherr.eu>
Date: Thu, 24 Oct 2024 22:32:14 +0200
Subject: [PATCH 3/3] improve coding style

---
 fractals/barnsley_farn.py | 39 ++++++++++++++++++++++++++++-----------
 1 file changed, 28 insertions(+), 11 deletions(-)

diff --git a/fractals/barnsley_farn.py b/fractals/barnsley_farn.py
index d2666157a2a6..3ad01f959784 100644
--- a/fractals/barnsley_farn.py
+++ b/fractals/barnsley_farn.py
@@ -16,40 +16,57 @@
 import numpy as np
 
 
-def barnsley_farn(n_points=100000):
+def barnsley_fern(n_points: int = 100000) -> np.ndarray:
     """
     Generates the points of the Barnsley fern.
+
+    Args:
+        n_points (int): Number of points to generate.
+
+    Returns:
+        np.ndarray: An array of shape (n_points, 2) containing the x and y coordinates.
     """
-    x, y = 0, 0
-    points = np.zeros((n_points, 2))
+    x, y = 0.0, 0.0
+    points = np.zeros((n_points, 2), dtype=np.float64)
 
     rng = np.random.default_rng()
 
     for i in range(n_points):
         r = rng.random()
         if r < 0.01:
-            x, y = 0, 0.16 * y
+            x, y = 0.0, 0.16 * y
         elif r < 0.86:
-            x, y = 0.85 * x + 0.04 * y, -0.04 * x + 0.85 * y + 1.6
+            x_new = 0.85 * x + 0.04 * y
+            y = -0.04 * x + 0.85 * y + 1.6
+            x = x_new
         elif r < 0.93:
-            x, y = 0.2 * x - 0.26 * y, 0.23 * x + 0.22 * y + 1.6
+            x_new = 0.20 * x - 0.26 * y
+            y = 0.23 * x + 0.22 * y + 1.6
+            x = x_new
         else:
-            x, y = -0.15 * x + 0.28 * y, 0.26 * x + 0.24 * y + 0.44
+            x_new = -0.15 * x + 0.28 * y
+            y = 0.26 * x + 0.24 * y + 0.44
+            x = x_new
         points[i] = [x, y]
 
     return points
 
 
-def plot_barnsley_farn(points):
+def plot_barnsley_fern(points: np.ndarray) -> None:
     """
     Plots the Barnsley fern using matplotlib.
+
+    Args:
+        points (np.ndarray): An array of shape (n_points, 2) containing coordinates.
     """
     x, y = points[:, 0], points[:, 1]
-    plt.scatter(x, y, s=0.1, color="green")
+    plt.figure(figsize=(6, 10))
+    plt.scatter(x, y, s=0.1, color="green", marker="o")
     plt.title("Barnsley Fern")
+    plt.axis("off")  # Hide the axes for better visualization
     plt.show()
 
 
 if __name__ == "__main__":
-    fern_points = barnsley_farn()
-    plot_barnsley_farn(fern_points)
+    fern_points = barnsley_fern()
+    plot_barnsley_fern(fern_points)