

'''simple docstring'''

import colorsys

from PIL import Image  # type: ignore




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 UpperCAmelCase	:     Optional[int]						 =			x
 UpperCAmelCase	:     List[Any]						 =			y
 for step in range(UpperCAmelCase_     ):  # noqa: B007
  UpperCAmelCase	:     Dict						 =			a * a - b * b + x
  UpperCAmelCase	:     Optional[Any]						 =			2 * a * b + y
  UpperCAmelCase	:     List[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(					UpperCAmelCase_     ):
 if distance == 1:
  return (0, 0, 0)
 else:
  return (2_55, 2_55, 2_55)




def 				UpperCamelCase(					UpperCAmelCase_     ):
 if distance == 1:
  return (0, 0, 0)
 else:
  return tuple(round(i * 2_55     ) for i in colorsys.hsv_to_rgb(UpperCAmelCase_  ,	1  ,	1     )     )




def 				UpperCamelCase(					UpperCAmelCase_ = 8_00  ,	UpperCAmelCase_ = 6_00  ,	UpperCAmelCase_ = -0.6  ,	UpperCAmelCase_ = 0  ,	UpperCAmelCase_ = 3.2  ,	UpperCAmelCase_ = 50  ,	UpperCAmelCase_ = True  ,	):
 UpperCAmelCase	:     List[Any]						 =			Image.new('RGB'  ,	(image_width, image_height)     )
 UpperCAmelCase	:     List[Any]						 =			img.load()

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

   UpperCAmelCase	:     Any						 =			get_distance(UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )

   # color the corresponding pixel based on the selected coloring-function
   if use_distance_color_coding:
    UpperCAmelCase	:     Optional[Any]						 =			get_color_coded_rgb(UpperCAmelCase_     )
   else:
    UpperCAmelCase	:     Optional[Any]						 =			get_black_and_white_rgb(UpperCAmelCase_     )

 return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 lowercase__         =      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 collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

lowercase__         =      TypeVar("KEY")
lowercase__         =      TypeVar("VAL")




@dataclass(frozen=_snake_case	,       slots=_snake_case							)
class 	A_			(    Generic[KEY, VAL]							):






     '''simple docstring'''



     UpperCAmelCase_						:     KEY
     UpperCAmelCase_						:     VAL




class 	A_			(    _Item							):






     '''simple docstring'''



     def __init__(		self			:					Any	)						->     None:
      super().__init__(lowercase_					,      lowercase_	)




     def __bool__(		self			:					List[str]	)						->     bool:
      return False



lowercase__         =      _DeletedItem()




class 	A_			(    MutableMapping[KEY, VAL]							):






     '''simple docstring'''



     def __init__(		self			:					Optional[int]					,      lowercase_			:					int = 8					,      lowercase_			:					float = 0.75	)						->     None:
      UpperCAmelCase	:     Dict						 =			initial_block_size
      UpperCAmelCase	:     list[_Item | None]						 =			[None] * initial_block_size
      assert 0.0 < capacity_factor < 1.0
      UpperCAmelCase	:     Any						 =			capacity_factor
      UpperCAmelCase	:     Union[str, Any]						 =			0


     def        UpperCAmelCase_	(		self			:					str					,      lowercase_			:					KEY	)						->     int:
      return hash(lowercase_	) % len(self._buckets	)


     def        UpperCAmelCase_	(		self			:					Any					,      lowercase_			:					int	)						->     int:
      return (ind + 1) % len(self._buckets	)


     def        UpperCAmelCase_	(		self			:					Dict					,      lowercase_			:					int					,      lowercase_			:					KEY					,      lowercase_			:					VAL	)						->     bool:
      UpperCAmelCase	:     List[Any]						 =			self._buckets[ind]
      if not stored:
       UpperCAmelCase	:     Dict						 =			_Item(lowercase_					,      lowercase_	)
       self._len += 1
       return True
      elif stored.key == key:
       UpperCAmelCase	:     Dict						 =			_Item(lowercase_					,      lowercase_	)
       return True
      else:
       return False


     def        UpperCAmelCase_	(		self			:					Any	)						->     bool:
      UpperCAmelCase	:     List[str]						 =			len(self._buckets	) * self._capacity_factor
      return len(self	) >= int(lowercase_	)


     def        UpperCAmelCase_	(		self			:					Optional[int]	)						->     bool:
      if len(self._buckets	) <= self._initial_block_size:
       return False
      UpperCAmelCase	:     Optional[int]						 =			len(self._buckets	) * self._capacity_factor / 2
      return len(self	) < limit


     def        UpperCAmelCase_	(		self			:					Dict					,      lowercase_			:					int	)						->     None:
      UpperCAmelCase	:     int						 =			self._buckets
      UpperCAmelCase	:     List[str]						 =			[None] * new_size
      UpperCAmelCase	:     Dict						 =			0
      for item in old_buckets:
       if item:
        self._add_item(item.key					,      item.val	)


     def        UpperCAmelCase_	(		self			:					Dict	)						->     None:
      self._resize(len(self._buckets	) * 2	)


     def        UpperCAmelCase_	(		self			:					Union[str, Any]	)						->     None:
      self._resize(len(self._buckets	) // 2	)


     def        UpperCAmelCase_	(		self			:					Union[str, Any]					,      lowercase_			:					KEY	)						->     Iterator[int]:
      UpperCAmelCase	:     Dict						 =			self._get_bucket_index(lowercase_	)
      for _ in range(len(self._buckets	)	):
       yield ind
       UpperCAmelCase	:     Union[str, Any]						 =			self._get_next_ind(lowercase_	)


     def        UpperCAmelCase_	(		self			:					Dict					,      lowercase_			:					KEY					,      lowercase_			:					VAL	)						->     None:
      for ind in self._iterate_buckets(lowercase_	):
       if self._try_set(lowercase_					,      lowercase_					,      lowercase_	):
        break


     def __setitem__(		self			:					Union[str, Any]					,      lowercase_			:					KEY					,      lowercase_			:					VAL	)						->     None:
      if self._is_full():
       self._size_up()

      self._add_item(lowercase_					,      lowercase_	)


     def __delitem__(		self			:					Tuple					,      lowercase_			:					KEY	)						->     None:
      for ind in self._iterate_buckets(lowercase_	):
       UpperCAmelCase	:     int						 =			self._buckets[ind]
       if item is None:
        raise KeyError(lowercase_	)
       if item is _deleted:
        continue
       if item.key == key:
        UpperCAmelCase	:     Union[str, Any]						 =			_deleted
        self._len -= 1
        break
      if self._is_sparse():
       self._size_down()


     def __getitem__(		self			:					Dict					,      lowercase_			:					KEY	)						->     VAL:
      for ind in self._iterate_buckets(lowercase_	):
       UpperCAmelCase	:     List[str]						 =			self._buckets[ind]
       if item is None:
        break
       if item is _deleted:
        continue
       if item.key == key:
        return item.val
      raise KeyError(lowercase_	)


     def __len__(		self			:					Optional[Any]	)						->     int:
      return self._len


     def __iter__(		self			:					int	)						->     Iterator[KEY]:
      yield from (item.key for item in self._buckets if item)




     def __repr__(		self			:					Optional[Any]	)						->     str:
      UpperCAmelCase	:     int						 =			' ,'.join(
          f"""{item.key}: {item.val}""" for item in self._buckets if item	)
      return f"""HashMap({val_string})"""




