22 lines
826 B
Python
22 lines
826 B
Python
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# Source: https://matplotlib.org/matplotblog/posts/animated-fractals/
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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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