breathaudio-backend/mandelbrot.py

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# Source: https://matplotlib.org/matplotblog/posts/animated-fractals/
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