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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 numpyiota(grid, T, l, savez):
"""
Calculates the ι using numpy arrays.
This works with both numpy.arrays and numpy.ndarrays
Also devides by l
:param grid: c-mesh. Shape will be used to make result
:param savez: Return z as the second element of returned tuple
"""
# Preallocate result array and z array
rs = np.zeros(grid.shape)
z = np.zeros(grid.shape)
# Calculate ι for all complex numbers
for i in range(l):
# This will generate warnings for some of the values rising above T.
# Because these values become NAN they are not used, thus the warnings
# can be ignored
z = z*z + grid
# This will generate 1 in all the places
# where z < T and zeros elsewhere
below = (np.abs(z) < T)
# Add this to the result
# Because the ones that pass T are 0
# they will stop counting.
#
# If a specific z never reaches >= T its value in rs will
# be l
rs += below
rs /= l
if not savez:
z = None
return (rs, 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
"""
# Used to calculate c-mesh
re = np.linspace(limitre[0], limitre[1], pre)
im = np.linspace(limitim[0], limitim[1], pim)
# Calculate c-mesh
grid = np.add.outer(re, 1j * im)
# Calculate ι
return numpyiota(grid, T, l, savez)
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