# -*- 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 = 120                             #maximum n for iterations (influences how detailed the structures are shown when zooming in)
x_min = """???"""                       #minimim value of x-interval
x_max = """???"""                       #maximum value of x-interval
y_min = """???"""                       #minimim value of y-interval
y_max = """???"""                       #maximum value of y-interval

a = np.linspace("""???""", detail, dtype=np.float64)  #define real axis [x_min, x_max]
b = np.linspace("""???""", detail, dtype=np.float64)  #define imaginary axis [y_min, y_max]

B = np.zeros((detail, detail))          #for color values n 

[x,y] = np.meshgrid("""???""")          #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("""???""", np.complex128)  #initial conditions (first iteration), Z has same dimension as C
for n in np.arange(1, maxit + 1):       #start iteration
  Z = """???"""                         #calculating Z
  expl = np.where("""???""")            #finding exploded values (i.e. with an absolute value > 2)
  Z[expl] = 0                           #removing from iteration
  C[expl] = 0                           #removing from plane
  B[expl] = """???"""                   #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')