Add barnsley fern

fractals/barnsley_farn.py

@@ -0,0 +1,72 @@
+"""
+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 matplotlib.pyplot as plt
+import numpy as np
+
+
+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, 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, 0.16 * y
+        elif r < 0.86:
+            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_new = 0.20 * x - 0.26 * y
+            y = 0.23 * x + 0.22 * y + 1.6
+            x = x_new
+        else:
+            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_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.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_fern()
+    plot_barnsley_fern(fern_points)