
"""simple docstring"""




import colorsys

from PIL import Image  # type: ignore

def lowercase_  (   _snake_case   ,_snake_case   ,_snake_case						):
							SCREAMING_SNAKE_CASE__						:       List[str]           =   x
							SCREAMING_SNAKE_CASE__						:       Optional[int]           =   y
							for step in range(_snake_case						):  # noqa: B007
														SCREAMING_SNAKE_CASE__						:       str           =   a * a - b * b + x
														SCREAMING_SNAKE_CASE__						:       str           =   2 * a * b + y
														SCREAMING_SNAKE_CASE__						:       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 lowercase_  (   _snake_case						):
							if distance == 1:
														return (0, 0, 0)
							else:
														return (255, 255, 255)

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

def lowercase_  (   _snake_case = 800   ,_snake_case = 600   ,_snake_case = -0.6   ,_snake_case = 0   ,_snake_case = 3.2   ,_snake_case = 50   ,_snake_case = True   ,):
							SCREAMING_SNAKE_CASE__						:       Tuple           =   Image.new("""RGB"""   ,(image_width, image_height)						)
							SCREAMING_SNAKE_CASE__						:       Dict           =   img.load()

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

																					SCREAMING_SNAKE_CASE__						:       str           =   get_distance(_snake_case   ,_snake_case   ,_snake_case						)

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

							return img


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# colored version, full figure
					UpperCAmelCase__      :    str    							= 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 math import pow, sqrt







def 						__a   (	*_SCREAMING_SNAKE_CASE   )	->bool:
  a__:     Union[str, Any]										=	len(_SCREAMING_SNAKE_CASE   ) > 0 and all(value > 0.0 for value in values   )
  return result







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(sqrt(molar_mass_a / molar_mass_a   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError('Input Error: Molar mass values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(effusion_rate * sqrt(molar_mass_a / molar_mass_a   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(effusion_rate / sqrt(molar_mass_a / molar_mass_a   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,     2   )		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )







def 						__a   (	_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )	->float | ValueError:
  return (
      round(pow(effusion_rate_a / effusion_rate_a		,     2   ) / molar_mass		,     6   )
      if validate(_SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE		,     _SCREAMING_SNAKE_CASE   )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.'   )
  )


