'''simple docstring'''




import colorsys

from PIL import Image  # type: ignore




def 							lowerCamelCase			(   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      int				)    ->   float:
							lowercase_      :    Union[str, Any]       		= x
							lowercase_      :    int       		= y
							for step in range(UpperCAmelCase__				):  # noqa: B007
														lowercase_      :    Tuple       		= a * a - b * b + x
														lowercase_      :    int       		= 2 * a * b + y
														lowercase_      :    List[str]       		= 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 							lowerCamelCase			(   UpperCAmelCase__ :      float				)    ->   tuple:
							if distance == 1:
														return (0, 0, 0)
							else:
														return (255, 255, 255)




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




def 							lowerCamelCase			(   UpperCAmelCase__ :      int = 800   ,   UpperCAmelCase__ :      int = 600   ,   UpperCAmelCase__ :      float = -0.6   ,   UpperCAmelCase__ :      float = 0   ,   UpperCAmelCase__ :      float = 3.2   ,   UpperCAmelCase__ :      int = 50   ,   UpperCAmelCase__ :      bool = True   ,   )    ->   Image.Image:
							lowercase_      :    str       		= Image.new("""RGB"""   ,   (image_width, image_height)				)
							lowercase_      :    int       		= 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
																					lowercase_      :    Dict       		= figure_width / image_width * image_height
																					lowercase_      :    Any       		= figure_center_x + (image_x / image_width - 0.5) * figure_width
																					lowercase_      :    Optional[int]       		= figure_center_y + (image_y / image_height - 0.5) * figure_height

																					lowercase_      :    List[Any]       		= get_distance(UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__				)

																					# color the corresponding pixel based on the selected coloring-function
																					if use_distance_color_coding:
																												lowercase_      :    Union[str, Any]       		= get_color_coded_rgb(UpperCAmelCase__				)
																					else:
																												lowercase_      :    Optional[Any]       		= get_black_and_white_rgb(UpperCAmelCase__				)

							return img


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						# colored version, full figure
						_lowercase		:				Dict	       =		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'''




_lowercase		:				int	       =		"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"




def 							lowerCamelCase			(   UpperCAmelCase__ :      bytes				)    ->   bytes:
							# Make sure the supplied data is a bytes-like object
							if not isinstance(UpperCAmelCase__   ,   UpperCAmelCase__				):
														lowercase_      :    Union[str, Any]       		= F'''a bytes-like object is required, not \'{data.__class__.__name__}\''''
														raise TypeError(UpperCAmelCase__				)

							lowercase_      :    Dict       		= """""".join(bin(UpperCAmelCase__				)[2:].zfill(8				) for byte in data				)

							lowercase_      :    Union[str, Any]       		= len(UpperCAmelCase__				) % 6 != 0

							if padding_needed:
														# The padding that will be added later
														lowercase_      :    List[Any]       		= b"""=""" * ((6 - len(UpperCAmelCase__				) % 6) // 2)

														# Append binary_stream with arbitrary binary digits (0's by default) to make its
														# length a multiple of 6.
														binary_stream += "0" * (6 - len(UpperCAmelCase__				) % 6)
							else:
														lowercase_      :    Union[str, Any]       		= b""""""

							# Encode every 6 binary digits to their corresponding Base64 character
							return (
							    "".join(
							        B64_CHARSET[int(binary_stream[index : index + 6]   ,   2				)]
							        for index in range(0   ,   len(UpperCAmelCase__				)   ,   6				)				).encode()
							    + padding
							)




def 							lowerCamelCase			(   UpperCAmelCase__ :      str				)    ->   bytes:
							# Make sure encoded_data is either a string or a bytes-like object
							if not isinstance(UpperCAmelCase__   ,   UpperCAmelCase__				) and not isinstance(UpperCAmelCase__   ,   UpperCAmelCase__				):
														lowercase_      :    List[str]       		= (
														    """argument should be a bytes-like object or ASCII string, """
														    F'''not \'{encoded_data.__class__.__name__}\''''
														)
														raise TypeError(UpperCAmelCase__				)

							# In case encoded_data is a bytes-like object, make sure it contains only
							# ASCII characters so we convert it to a string object
							if isinstance(UpperCAmelCase__   ,   UpperCAmelCase__				):
														try:
																					lowercase_      :    Optional[int]       		= encoded_data.decode("""utf-8"""				)
														except UnicodeDecodeError:
																					raise ValueError("""base64 encoded data should only contain ASCII characters"""				)

							lowercase_      :    Any       		= encoded_data.count("""="""				)

							# Check if the encoded string contains non base64 characters
							if padding:
														assert all(
														    char in B64_CHARSET for char in encoded_data[:-padding]				), "Invalid base64 character(s) found."
							else:
														assert all(
														    char in B64_CHARSET for char in encoded_data				), "Invalid base64 character(s) found."

							# Check the padding
							assert len(UpperCAmelCase__				) % 4 == 0 and padding < 3, "Incorrect padding"

							if padding:
														# Remove padding if there is one
														lowercase_      :    Optional[int]       		= encoded_data[:-padding]

														lowercase_      :    Any       		= """""".join(
														    bin(B64_CHARSET.index(UpperCAmelCase__				)				)[2:].zfill(6				) for char in encoded_data				)[: -padding * 2]
							else:
														lowercase_      :    int       		= """""".join(
														    bin(B64_CHARSET.index(UpperCAmelCase__				)				)[2:].zfill(6				) for char in encoded_data				)

							lowercase_      :    Optional[int]       		= [
							    int(binary_stream[index : index + 8]   ,   2				)
							    for index in range(0   ,   len(UpperCAmelCase__				)   ,   8				)
							]

							return bytes(UpperCAmelCase__				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()





