Solved Task 3

Schenk_Brandenberger_S11_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: knaa
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+detail = 1000                       #number of pixels in x and y direction
+maxit = 70                          #maximum n for iterations
+x_min = -2                          #minimim value of x-interval
+x_max = 0.7                         #maximum value of x-interval
+y_min = -1.4                        #minimim vale of y-interval
+y_max = 1.4                         #minimim vale 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 valzues n
+
+[x,y] = np.meshgrid(a, b)                            #to create the complex plane with the axes defined by a and b
+C = x+y*1j                                           #creating the plane
+Z = np.zeros((detail, detail), np.complex64)         #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) > 2.0)                   #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))           #deviding by max value for correct color
+plt.imshow(B,extent=[x_min,x_max,y_min,y_max],origin='lower',interpolation='bilinear')   #display image
+
+plt.show()