



import colorsys

from PIL import Image  # type: ignore



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



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



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	int = 800				,       SCREAMING_SNAKE_CASE__       :	int = 600				,       SCREAMING_SNAKE_CASE__       :	float = -0.6				,       SCREAMING_SNAKE_CASE__       :	float = 0				,       SCREAMING_SNAKE_CASE__       :	float = 3.2				,       SCREAMING_SNAKE_CASE__       :	int = 50				,       SCREAMING_SNAKE_CASE__       :	bool = True				,       )  ->     Image.Image:
	_snake_case    :  List[str]					=					Image.new("""RGB"""				,       (image_width, image_height)				)
	_snake_case    :  List[str]					=					img.load()

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

			_snake_case    :  Optional[int]					=					get_distance(SCREAMING_SNAKE_CASE__				,       SCREAMING_SNAKE_CASE__				,       SCREAMING_SNAKE_CASE__				)

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

	return img


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		# colored version, full figure
		a__    =	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 __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
a__    =	1.0_54_57_18_17E-34  # unit of ℏ : J * s

a__    =	3E8  # unit of c : m * s^-1



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	float				,       SCREAMING_SNAKE_CASE__       :	float				,       SCREAMING_SNAKE_CASE__       :	float				)  ->     dict[str, float]:

 if (force, area, distance).count(0				) != 1:
  raise ValueError("""One and only one argument must be 0"""				)
 if force < 0:
  raise ValueError("""Magnitude of force can not be negative"""				)
 if distance < 0:
  raise ValueError("""Distance can not be negative"""				)
 if area < 0:
  raise ValueError("""Area can not be negative"""				)
 if force == 0:
  _snake_case    :  Union[str, Any]					=					(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
      240 * (distance) ** 4
  )
  return {"force": force}
 elif area == 0:
  _snake_case    :  Optional[Any]					=					(240 * force * (distance) ** 4) / (
      REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
  )
  return {"area": area}
 elif distance == 0:
  _snake_case    :  str					=					(
      (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
  ) ** (1 / 4)
  return {"distance": distance}
 raise ValueError("""One and only one argument must be 0"""				)


# Run doctest
if __name__ == "__main__":
  import doctest

  doctest.testmod()
