




import colorsys

from PIL import Image  # type: ignore




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				__magic_name__						:						Any										=x
				__magic_name__						:						Dict										=y
				for step in range(lowerCamelCase ):  # noqa: B007
								__magic_name__						:						str										=a * a - b * b + x
								__magic_name__						:						int										=2 * a * b + y
								__magic_name__						:						Union[str, 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 		lowerCAmelCase_ (						lowerCamelCase ):
				if distance == 1:
								return (0, 0, 0)
				else:
								return (255, 255, 255)




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




def 		lowerCAmelCase_ (						lowerCamelCase = 800						,  lowerCamelCase = 600						,  lowerCamelCase = -0.6						,  lowerCamelCase = 0						,  lowerCamelCase = 3.2						,  lowerCamelCase = 50						,  lowerCamelCase = True						,  ):
				__magic_name__						:						Tuple										=Image.new("""RGB"""						,  (image_width, image_height) )
				__magic_name__						:						List[Any]										=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
												__magic_name__						:						Optional[int]										=figure_width / image_width * image_height
												__magic_name__						:						Optional[int]										=figure_center_x + (image_x / image_width - 0.5) * figure_width
												__magic_name__						:						Tuple										=figure_center_y + (image_y / image_height - 0.5) * figure_height

												__magic_name__						:						Optional[int]										=get_distance(lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase )

												# color the corresponding pixel based on the selected coloring-function
												if use_distance_color_coding:
																__magic_name__						:						Optional[int]										=get_color_coded_rgb(lowerCamelCase )
												else:
																__magic_name__						:						int										=get_black_and_white_rgb(lowerCamelCase )

				return img


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# colored version, full figure
							UpperCAmelCase_		:					Any          =  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'''

import baseaa







def __UpperCamelCase( _A       :					str     ):
   '''simple docstring'''
   return baseaa.baaencode(string.encode('''utf-8'''     )     )







def __UpperCamelCase( _A       :					bytes     ):
   '''simple docstring'''
   return baseaa.baadecode(_A     ).decode('''utf-8'''     )


if __name__ == "__main__":
  UpperCamelCase__  :						List[str]					=      'Hello World!'
  UpperCamelCase__  :						str					=      baseaa_encode(test)
  print(encoded)

  UpperCamelCase__  :						int					=      baseaa_decode(encoded)
  print(decoded)




