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Python/mandelbrot.py

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+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.animation as animation
+
+def mandelbrot(x, y, threshold):
+    """Calculates whether the number c = x + i*y belongs to the 
+    Mandelbrot set. In order to belong, the sequence z[i + 1] = z[i]**2 + c
+    must not diverge after 'threshold' number of steps. The sequence diverges
+    if the absolute value of z[i+1] is greater than 4.
+    
+    :param float x: the x component of the initial complex number
+    :param float y: the y component of the initial complex number
+    :param int threshold: the number of iterations to considered it converged
+    """
+    # initial conditions
+    c = complex(x, y)
+    z = complex(0, 0)
+    
+    for i in range(threshold):
+        z = z**2 + c
+        if abs(z) > 4.:  # it diverged
+            return i
+        
+    return threshold - 1  # it didn't diverge
+
+
+x_start, y_start = -2, -1.5  # an interesting region starts here
+width, height = 3, 3  # for 3 units up and right
+density_per_unit = 250  # how many pixles per unit
+
+# real and imaginary axis
+re = np.linspace(x_start, x_start + width, width * density_per_unit )
+im = np.linspace(y_start, y_start + height, height * density_per_unit)
+
+fig = plt.figure(figsize=(10, 10))  # instantiate a figure to draw
+ax = plt.axes()  # create an axes object
+
+def animate(i):
+    print(i)
+    ax.clear()  # clear axes object
+    ax.set_xticks([])  # clear x-axis ticks
+    ax.set_yticks([])  # clear y-axis ticks
+
+    X = np.empty((len(re), len(im)))  # re-initialize the array-like image
+    threshold = round(1.25**(i + 1))  # calculate the current threshold
+
+    # iterations for the current threshold
+    for i in range(len(re)):
+        for j in range(len(im)):
+            X[i, j] = mandelbrot(re[i], im[j], threshold)
+
+    # associate colors to the iterations with an iterpolation
+    img = ax.imshow(X.T, interpolation="bicubic", cmap='Reds')
+    return [img]
+
+anim = animation.FuncAnimation(fig, animate, frames=45, interval=16, blit=True)
+anim.save('mandelbrot.gif',writer='imagemagick')
+print("Done")