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import numpy as np
import matplotlib.pyplot as plt
import time
# c-mesh limits
limitre = ( -2, 1 )
limitim = ( -1.5, 1.5 )
def iota(c, T, l):
"""
Implement the ι function used in mangelbrot
Also devides by l
:param c: Complex number from the c-mesh
:param T: Mangelbrot threshold
:param l: Iterations
"""
z = 0
for i in range(l):
z = z*z + c
# Check if we found or z
if np.abs(z) > T:
return (i / l, z)
# If we did not find z, use l
return (l / l, z)
def mangel(pre, pim, T, l, savez):
"""
Calculate the mangelbrot image
(pre, pim) discribes the image size. Use T and l to tune the mangelbrot
This function uses the global variables limitre and limitim to determine
the c-mesh range.
:param pre: Number of real numbers used
:param pim: Number of imaginary numbers
:param T: Mangelbrot threshold
:param l: Iterations
:param savez: Return z as the second element of returned tuple
"""
# Preallocate result array
rs = np.zeros((pre, pim))
z = np.empty((pre, pim), dtype=complex)
# Calculate scaling variables
sre = ( limitre[1] - limitre[0] ) / (pre-1)
sim = ( limitim[1] - limitim[0] ) / (pim-1)
# Loop all pixels
for re in range(pre):
for im in range(pim):
# Calculate the complex number using the scalers
c = limitre[0] + limitim[0] * 1j + sre * re + 1j * sim * im
# Calculate the ι
(rs[re,im], z[re, im]) = iota(c, T, l)
if savez:
return (rs, z)
else:
return (rs, None)
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