Add barnsley fern

fractals/barnsley_farn.py

@@ -0,0 +1,55 @@
+"""
+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_farn(n_points=100000):
+    """
+    Generates the points of the Barnsley fern.
+    """
+    x, y = 0, 0
+    points = np.zeros((n_points, 2))
+
+    rng = np.random.default_rng()
+
+    for i in range(n_points):
+        r = rng.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)