
import colorsys

from PIL import Image  # type: ignore




def        __UpperCamelCase					(    lowerCAmelCase__							:    float  ,       lowerCAmelCase__							:    float  ,       lowerCAmelCase__							:    int  ):






 """simple docstring"""




 __a			:  int		    =  x
 __a			:  Dict		    =  y
 for step in range(lowerCAmelCase__  ):  # noqa: B007
  __a			:  Optional[int]		    =  a * a - b * b + x
  __a			:  Union[str, Any]		    =  2 * a * b + y
  __a			:  Dict		    =  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__							:    float  ):






 """simple docstring"""




 if distance == 1:
  return (0, 0, 0)
 else:
  return (2_5_5, 2_5_5, 2_5_5)




def        __UpperCamelCase					(    lowerCAmelCase__							:    float  ):






 """simple docstring"""




 if distance == 1:
  return (0, 0, 0)
 else:
  return tuple(round(i * 2_5_5  ) for i in colorsys.hsv_to_rgb(lowerCAmelCase__  ,       1  ,       1  )  )




def        __UpperCamelCase					(    lowerCAmelCase__							:    int = 8_0_0  ,       lowerCAmelCase__							:    int = 6_0_0  ,       lowerCAmelCase__							:    float = -0.6  ,       lowerCAmelCase__							:    float = 0  ,       lowerCAmelCase__							:    float = 3.2  ,       lowerCAmelCase__							:    int = 5_0  ,       lowerCAmelCase__							:    bool = True  ,       ):






 """simple docstring"""




 __a			:  List[Any]		    =  Image.new('''RGB'''  ,       (image_width, image_height)  )
 __a			:  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
   __a			:  List[Any]		    =  figure_width / image_width * image_height
   __a			:  Tuple		    =  figure_center_x + (image_x / image_width - 0.5) * figure_width
   __a			:  Optional[Any]		    =  figure_center_y + (image_y / image_height - 0.5) * figure_height

   __a			:  Dict		    =  get_distance(lowerCAmelCase__  ,       lowerCAmelCase__  ,       lowerCAmelCase__  )

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

 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()


from math import pi, sqrt




def        __UpperCamelCase					(    lowerCAmelCase__							:    float  ):
 if num <= 0:
  raise ValueError('''math domain error'''  )
 if num > 1_71.5:
  raise OverflowError('''math range error'''  )
 elif num - int(lowerCAmelCase__  ) not in (0, 0.5):
  raise NotImplementedError('''num must be an integer or a half-integer'''  )
 elif num == 0.5:
  return sqrt(lowerCAmelCase__  )
 else:
  return 1.0 if num == 1 else (num - 1) * gamma(num - 1  )




def        __UpperCamelCase					(    ):
 assert gamma(0.5  ) == sqrt(lowerCAmelCase__  )
 assert gamma(1  ) == 1.0
 assert gamma(2  ) == 1.0


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

      testmod()
      lowercase__          =1.0
      while num:
            lowercase__          =float(input('Gamma of: '))
            print(F"""gamma({num}) = {gamma(num)}""")
            print('\nEnter 0 to exit...')
