40 lines
1.8 KiB
Python
40 lines
1.8 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Created on Sun Nov 29 14:43:17 2020
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Höhere Mathematik 1, Serie 11, Aufgabe 3 (Gerüst)
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@author: kuengjoe
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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detail = 1000 # number of pixels in x and y direction
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maxit = 120 # maximum n for iterations (influences how detailed the structures are shown when zooming in)
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x_min = -2.0 # minimum value of x-interval
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x_max = 0.7 # maximum value of x-interval
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y_min = -1.4 # minimum value of y-interval
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y_max = 1.4 # maximum value of y-interval
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a = np.linspace(x_min, x_max, detail, dtype=np.float64) # define real axis [x_min, x_max]
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b = np.linspace(y_min, y_max, detail, dtype=np.float64) # define imaginary axis [y_min, y_max]
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B = np.zeros((detail, detail)) # for color values n
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[x, y] = np.meshgrid(a, b) # to create the complex plane with the axes defined by a and b
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C = np.array(x + y*1j, np.complex128) # creating the plane
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Z = np.zeros(C.shape, np.complex128) # initial conditions (first iteration), Z has same dimension as C
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for n in np.arange(1, maxit + 1): # start iteration
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Z = Z**2 + C # calculating Z
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expl = np.where(np.abs(Z) > 2) # finding exploded values (i.e. with an absolute value > 2)
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Z[expl] = 0 # removing from iteration
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C[expl] = 0 # removing from plane
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B[expl] = n # saving color value n
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plt.figure(1)
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B = B/np.max(np.max(B)) # dividing by max value for correct color
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# display image
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plt.imshow(B, extent=[x_min, x_max, y_min, y_max], origin='lower', interpolation='bilinear')
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plt.show()
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