Serie 11 and 12

Kuengjoe_S11/Kuengjoe_S10_Aufg3.py

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