code: 
  
  
  '''simple docstring'''
  
  
  
  
  import warnings
  from collections.abc import Callable
  from typing import Any
  
  import numpy
  from matplotlib import pyplot
  
  __lowercase  :      List[str]      		=				0.25 + 0.0j
  __lowercase  :      Union[str, Any]      		=				-0.4 + 0.6j
  __lowercase  :      Optional[int]      		=				-0.1 + 0.651j
  __lowercase  :      Dict      		=				-2.0
  __lowercase  :      int      		=				56
  __lowercase  :      Optional[Any]      		=				2.0
  __lowercase  :      Dict      		=				6_66
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->Optional[int]:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return numpy.exp(UpperCamelCase_    ) + c_parameter
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->str:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return z_values * z_values + c_parameter
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase    )			->Tuple:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Dict											=					numpy.linspace(-window_size							,						UpperCamelCase_							,						UpperCamelCase_    )
  				__lowerCamelCase		:      Optional[Any]											=					x.reshape((nb_pixels, 1)    )
  				__lowerCamelCase		:      List[str]											=					numpy.linspace(-window_size							,						UpperCamelCase_							,						UpperCamelCase_    )
  				__lowerCamelCase		:      Optional[int]											=					y.reshape((1, nb_pixels)    )
  				return x + 1.0J * y
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase							,						lowercase							,						lowercase							,						lowercase = None							,						)			->List[str]:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      Optional[Any]											=					z_a.astype("complex64"    )
  				for _ in range(UpperCamelCase_    ):
  								__lowerCamelCase		:      Any											=					eval_function(UpperCamelCase_							,						UpperCamelCase_    )
  								if infinity is not None:
  												numpy.nan_to_num(UpperCamelCase_							,						copy=UpperCamelCase_							,						nan=UpperCamelCase_    )
  												__lowerCamelCase		:      str											=					infinity
  				return z_n
  
  
  
  
  
  def 							a_       (						lowercase							,						lowercase							,						lowercase							,						lowercase							,						)			->List[Any]:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				__lowerCamelCase		:      str											=					(abs(UpperCamelCase_    )).transpose()
  				__lowerCamelCase		:      List[Any]											=					abs_z_final[::-1, :]
  				pyplot.matshow(abs_z_final < escape_radius    )
  				pyplot.title(F'Julia set of ${function_label}$, $c={function_params}$'    )
  				pyplot.show()
  
  
  
  
  
  def 							a_       (						)			->Tuple:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				warnings.filterwarnings(
  				    "ignore"							,						category=UpperCamelCase_							,						message="overflow encountered in multiply"    )
  				warnings.filterwarnings(
  				    "ignore"							,						category=UpperCamelCase_							,						message="invalid value encountered in multiply"							,						)
  				warnings.filterwarnings(
  				    "ignore"							,						category=UpperCamelCase_							,						message="overflow encountered in absolute"    )
  				warnings.filterwarnings(
  				    "ignore"							,						category=UpperCamelCase_							,						message="overflow encountered in exp"    )
  
  
  if __name__ == "__main__":
  				__lowercase  :      str      		=				prepare_grid(window_size, nb_pixels)
  
  				ignore_overflow_warnings()  # See file header for explanations
  
  				__lowercase  :      Any      		=				24
  				__lowercase  :      Dict      		=				2 * abs(c_cauliflower) + 1
  				__lowercase  :      Optional[Any]      		=				iterate_function(
  				    eval_quadratic_polynomial,
  				    c_cauliflower,
  				    nb_iterations,
  				    z_a,
  				    infinity=1.1 * escape_radius,
  				)
  				show_results("""z^2+c""", c_cauliflower, escape_radius, z_final)
  
  				__lowercase  :      List[str]      		=				64
  				__lowercase  :      Any      		=				2 * abs(c_polynomial_a) + 1
  				__lowercase  :      List[str]      		=				iterate_function(
  				    eval_quadratic_polynomial,
  				    c_polynomial_a,
  				    nb_iterations,
  				    z_a,
  				    infinity=1.1 * escape_radius,
  				)
  				show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)
  
  				__lowercase  :      List[Any]      		=				1_61
  				__lowercase  :      List[Any]      		=				2 * abs(c_polynomial_a) + 1
  				__lowercase  :      Dict      		=				iterate_function(
  				    eval_quadratic_polynomial,
  				    c_polynomial_a,
  				    nb_iterations,
  				    z_a,
  				    infinity=1.1 * escape_radius,
  				)
  				show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)
  
  				__lowercase  :      Optional[Any]      		=				12
  				__lowercase  :      Dict      		=				1_00_00.0
  				__lowercase  :      Tuple      		=				iterate_function(
  				    eval_exponential,
  				    c_exponential,
  				    nb_iterations,
  				    z_a + 2,
  				    infinity=1.0e10,
  				)
  				show_results("""e^z+c""", c_exponential, escape_radius, z_final)
  
  
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  
  def 							a_       (						lowercase    )			->str:
  
  
  
  
  
  
  				'''simple docstring'''
  
  				return " ".join(sorted(set(sentence.split()    )    )    )
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  
  
  
  
  