


import colorsys

from PIL import Image  # type: ignore



def 				UpperCamelCase_(      lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )    ->						float:
    _lowercase       :							str      		=		x
    _lowercase       :							int      		=		y
    for step in range(lowerCamelCase_ ):  # noqa: B007
        _lowercase       :							Optional[Any]      		=		a * a - b * b + x
        _lowercase       :							List[str]      		=		2 * a * b + y
        _lowercase       :							Optional[Any]      		=		a_new

        # divergence happens for all complex number with an absolute value
        # greater than 4
        if a * a + b * b > 4:
            break
    return step / (max_step - 1)



def 				UpperCamelCase_(      lowerCamelCase_ )    ->						tuple:
    if distance == 1:
        return (0, 0, 0)
    else:
        return (255, 255, 255)



def 				UpperCamelCase_(      lowerCamelCase_ )    ->						tuple:
    if distance == 1:
        return (0, 0, 0)
    else:
        return tuple(round(i * 255 ) for i in colorsys.hsv_to_rgb(lowerCamelCase_							, 1							, 1 ) )



def 				UpperCamelCase_(      lowerCamelCase_ = 800							, lowerCamelCase_ = 600							, lowerCamelCase_ = -0.6							, lowerCamelCase_ = 0							, lowerCamelCase_ = 3.2							, lowerCamelCase_ = 50							, lowerCamelCase_ = True							, )    ->						Image.Image:
    _lowercase       :							Optional[Any]      		=		Image.new('RGB'							, (image_width, image_height) )
    _lowercase       :							str      		=		img.load()

    # loop through the image-coordinates
    for image_x in range(lowerCamelCase_ ):
        for image_y in range(lowerCamelCase_ ):
            # determine the figure-coordinates based on the image-coordinates
            _lowercase       :							Dict      		=		figure_width / image_width * image_height
            _lowercase       :							Union[str, Any]      		=		figure_center_x + (image_x / image_width - 0.5) * figure_width
            _lowercase       :							List[Any]      		=		figure_center_y + (image_y / image_height - 0.5) * figure_height

            _lowercase       :							Any      		=		get_distance(lowerCamelCase_							, lowerCamelCase_							, lowerCamelCase_ )

            # color the corresponding pixel based on the selected coloring-function
            if use_distance_color_coding:
                _lowercase       :							Dict      		=		get_color_coded_rgb(lowerCamelCase_ )
            else:
                _lowercase       :							Any      		=		get_black_and_white_rgb(lowerCamelCase_ )

    return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 SCREAMING_SNAKE_CASE       :      int												= get_image()

 # uncomment for colored version, different section, zoomed in
 # img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
 # figure_width = 0.8)

 # uncomment for black and white version, full figure
 # img = get_image(use_distance_color_coding = False)

 # uncomment to save the image
 # img.save("mandelbrot.png")

 img.show()




'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

__lowerCAmelCase         =    TypeVar("""T""")







class UpperCAmelCase__	( Generic[T]	):





  """simple docstring"""

  def __init__(		self      :     Tuple							,_a      :     T       ):


     '''simple docstring'''






     _a				:	List[str]			=   data
     _a				:	Node[T] | None			=   None


  def __str__(		self      :     Dict       ):


     '''simple docstring'''






     return F"""{self.data}"""







class UpperCAmelCase__	( Generic[T]	):





  """simple docstring"""

  def __init__(		self      :     Optional[int]       ):


     '''simple docstring'''






     _a				:	Node[T] | None			=   None


  def __iter__(		self      :     str       ):


     '''simple docstring'''






     _a				:	Tuple			=   self.top
     while node:
        yield node.data
        _a				:	int			=   node.next


  def __str__(		self      :     str       ):


     '''simple docstring'''






     return "->".join([str(_a       ) for item in self]       )


  def __len__(		self      :     Optional[Any]       ):


     '''simple docstring'''






     return len(tuple(iter(self       )       )       )


  def   __lowercase		(		self      :     str       ):


     '''simple docstring'''






     return self.top is None


  def   __lowercase		(		self      :     List[Any]							,_a      :     T       ):


     '''simple docstring'''






     _a				:	int			=   Node(_a       )
     if not self.is_empty():
        _a				:	Optional[Any]			=   self.top
     _a				:	List[str]			=   node


  def   __lowercase		(		self      :     Tuple       ):


     '''simple docstring'''






     if self.is_empty():
        raise IndexError('pop from empty stack'       )
     assert isinstance(self.top							,_a       )
     _a				:	List[Any]			=   self.top
     _a				:	int			=   self.top.next
     return pop_node.data


  def   __lowercase		(		self      :     List[str]       ):


     '''simple docstring'''






     if self.is_empty():
        raise IndexError('peek from empty stack'       )

     assert self.top is not None
     return self.top.data


  def   __lowercase		(		self      :     List[str]       ):


     '''simple docstring'''






     _a				:	Optional[int]			=   None


if __name__ == "__main__":
  from doctest import testmod

  testmod()



