# -*- 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()