


'''simple docstring'''






def 		_A			(lowerCAmelCase__					:int			,  lowerCAmelCase__					:int						)				->					str:




     '''simple docstring'''



     if a < 0 or b < 0:
          raise ValueError('the value of both inputs must be positive'						)
     _a      =							str(bin(lowerCAmelCase__						)						)[2:]  # remove the leading "0b"
     _a      =							str(bin(lowerCAmelCase__						)						)[2:]
     _a      =							max(len(lowerCAmelCase__						)			,  len(lowerCAmelCase__						)						)
     return "0b" + "".join(
         str(int('1' in (char_a, char_b)						)						)
         for char_a, char_b in zip(a_binary.zfill(lowerCAmelCase__						)			,  b_binary.zfill(lowerCAmelCase__						)						)						)


if __name__ == "__main__":
 import doctest

 doctest.testmod()









'''simple docstring'''






import colorsys

from PIL import Image  # type: ignore






def 		_A			(lowerCAmelCase__					:float			,  lowerCAmelCase__					:float			,  lowerCAmelCase__					:int						)				->					float:




     '''simple docstring'''



     _a      =							x
     _a      =							y
     for step in range(lowerCAmelCase__						):  # noqa: B007
          _a      =							a * a - b * b + x
          _a      =							2 * a * b + y
          _a      =							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 		_A			(lowerCAmelCase__					:float						)				->					tuple:




     '''simple docstring'''



     if distance == 1:
          return (0, 0, 0)
     else:
          return (2_55, 2_55, 2_55)






def 		_A			(lowerCAmelCase__					:float						)				->					tuple:




     '''simple docstring'''



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






def 		_A			(lowerCAmelCase__					:int = 8_00			,  lowerCAmelCase__					:int = 6_00			,  lowerCAmelCase__					:float = -0.6			,  lowerCAmelCase__					:float = 0			,  lowerCAmelCase__					:float = 3.2			,  lowerCAmelCase__					:int = 50			,  lowerCAmelCase__					:bool = True			,  )				->					Image.Image:




     '''simple docstring'''



     _a      =							Image.new('RGB'			,  (image_width, image_height)						)
     _a      =							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
               _a      =							figure_width / image_width * image_height
               _a      =							figure_center_x + (image_x / image_width - 0.5) * figure_width
               _a      =							figure_center_y + (image_y / image_height - 0.5) * figure_height

               _a      =							get_distance(lowerCAmelCase__			,  lowerCAmelCase__			,  lowerCAmelCase__						)

               # color the corresponding pixel based on the selected coloring-function
               if use_distance_color_coding:
                    _a      =							get_color_coded_rgb(lowerCAmelCase__						)
               else:
                    _a      =							get_black_and_white_rgb(lowerCAmelCase__						)

     return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 a_   :      Optional[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()

