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