code: 
  
  import warnings
  from collections.abc import Callable
  from typing import Any
  
  import numpy
  from matplotlib import pyplot
  
  snake_case_    						=				0.25 + 0.0j
  snake_case_    						=				-0.4 + 0.6j
  snake_case_    						=				-0.1 + 0.6_5_1j
  snake_case_    						=				-2.0
  snake_case_    						=				56
  snake_case_    						=				2.0
  snake_case_    						=				666
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					complex			,  SCREAMING_SNAKE_CASE_	:					numpy.ndarray    ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       return numpy.exp(SCREAMING_SNAKE_CASE_    ) + c_parameter
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					complex			,  SCREAMING_SNAKE_CASE_	:					numpy.ndarray    ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       return z_values * z_values + c_parameter
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					float			,  SCREAMING_SNAKE_CASE_	:					int    ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       lowercase__					:     List[Any]   = numpy.linspace(-window_size			,  SCREAMING_SNAKE_CASE_			,  SCREAMING_SNAKE_CASE_    )
       lowercase__					:     Any   = x.reshape((nb_pixels, 1)    )
       lowercase__					:     List[str]   = numpy.linspace(-window_size			,  SCREAMING_SNAKE_CASE_			,  SCREAMING_SNAKE_CASE_    )
       lowercase__					:     int   = y.reshape((1, nb_pixels)    )
       return x + 1.0J * y
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					Callable[[Any, numpy.ndarray], numpy.ndarray]			,  SCREAMING_SNAKE_CASE_	:					Any			,  SCREAMING_SNAKE_CASE_	:					int			,  SCREAMING_SNAKE_CASE_	:					numpy.ndarray			,  SCREAMING_SNAKE_CASE_	:					float | None = None			,  ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       lowercase__					:     Optional[int]   = z_a.astype('complex64'    )
       for _ in range(SCREAMING_SNAKE_CASE_    ):
            lowercase__					:     List[Any]   = eval_function(SCREAMING_SNAKE_CASE_			,  SCREAMING_SNAKE_CASE_    )
            if infinity is not None:
                 numpy.nan_to_num(SCREAMING_SNAKE_CASE_			,  copy=SCREAMING_SNAKE_CASE_			,  nan=SCREAMING_SNAKE_CASE_    )
                 lowercase__					:     str   = infinity
       return z_n
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					str			,  SCREAMING_SNAKE_CASE_	:					Any			,  SCREAMING_SNAKE_CASE_	:					float			,  SCREAMING_SNAKE_CASE_	:					numpy.ndarray			,  ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       lowercase__					:     List[Any]   = (abs(SCREAMING_SNAKE_CASE_    )).transpose()
       lowercase__					:     Dict   = 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 			snake_case__    (					):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       warnings.filterwarnings(
           'ignore'			,  category=SCREAMING_SNAKE_CASE_			,  message='overflow encountered in multiply'    )
       warnings.filterwarnings(
           'ignore'			,  category=SCREAMING_SNAKE_CASE_			,  message='invalid value encountered in multiply'			,  )
       warnings.filterwarnings(
           'ignore'			,  category=SCREAMING_SNAKE_CASE_			,  message='overflow encountered in absolute'    )
       warnings.filterwarnings(
           'ignore'			,  category=SCREAMING_SNAKE_CASE_			,  message='overflow encountered in exp'    )
  
  
  if __name__ == "__main__":
         snake_case_    						=				prepare_grid(window_size, nb_pixels)
  
         ignore_overflow_warnings()  # See file header for explanations
  
         snake_case_    						=				24
         snake_case_    						=				2 * abs(c_cauliflower) + 1
         snake_case_    						=				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)
  
         snake_case_    						=				64
         snake_case_    						=				2 * abs(c_polynomial_a) + 1
         snake_case_    						=				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)
  
         snake_case_    						=				161
         snake_case_    						=				2 * abs(c_polynomial_a) + 1
         snake_case_    						=				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)
  
         snake_case_    						=				12
         snake_case_    						=				1_0000.0
         snake_case_    						=				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: 
  
  from __future__ import annotations
  
  
  class    SCREAMING_SNAKE_CASE__      :
  
  
  
  
  
      def __init__(   self		,     a = 0):
           lowercase__					:     int   = value
           lowercase__					:     Node | None   = None
           lowercase__					:     Node | None   = None
  
  
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					Node | None			,  SCREAMING_SNAKE_CASE_	:					Node | None    ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       if treea is None:
            return treea
       if treea is None:
            return treea
  
       lowercase__					:     Optional[Any]   = treea.value + treea.value
       lowercase__					:     Union[str, Any]   = merge_two_binary_trees(treea.left			,  treea.left    )
       lowercase__					:     Optional[Any]   = merge_two_binary_trees(treea.right			,  treea.right    )
       return treea
  
  def 			snake_case__    (					SCREAMING_SNAKE_CASE_	:					Node | None    ):
  
  
  
       '''simple docstring'''
  
  
  
  
  
       if root:
            print(root.value    )
            print_preorder(root.left    )
            print_preorder(root.right    )
  
  
  if __name__ == "__main__":
         snake_case_    						=				Node(1)
         snake_case_    						=				Node(2)
         snake_case_    						=				Node(3)
         snake_case_    						=				Node(4)
  
         snake_case_    						=				Node(2)
         snake_case_    						=				Node(4)
         snake_case_    						=				Node(6)
         snake_case_    						=				Node(9)
         snake_case_    						=				Node(5)
  
         print('''Tree1 is: ''')
         print_preorder(treea)
         print('''Tree2 is: ''')
         print_preorder(treea)
         snake_case_    						=				merge_two_binary_trees(treea, treea)
         print('''Merged Tree is: ''')
         print_preorder(merged_tree)
  
  