text: '''
  ANKIT KHANDELWAL
  15863
  
  Exercise 15
  '''
  
  import math
  
  import matplotlib.pyplot as plt
  import numpy as np
  
  x = np.linspace(-2, 2, 2000)
  y = np.linspace(-2, 2, 2000)
  x_final = []
  y_final = []
  Re_z = 0
  Im_z = 0
  for Re_c in x:
      for Im_c in y:
          for i in range(0, 100):
              Re_z1 = Re_z ** 2 - Im_z ** 2 + Re_c
              Im_z1 = 2 * Re_z * Im_z + Im_c
              mod_z1 = math.sqrt(Re_z1 ** 2 + Im_z1 ** 2)
              if mod_z1 > 2:
                  break
              Re_z = Re_z1
              Im_z = Im_z1
          if mod_z1 < 2:
              x_final.append(Re_c)
              y_final.append(Im_c)
          Re_z = 0
          Im_z = 0
  plt.plot(x_final, y_final, 'k.')
  plt.xlabel('Real part of c')
  plt.ylabel('Imaginary part of c')
  plt.show()
  