
import colorsys

from PIL import Image  # type: ignore


def    A (      lowercase					, lowercase					, lowercase				)     ->						float:
		'''simple docstring'''

		UpperCamelCase						=  x
		UpperCamelCase						=  y
		for step in range(lowercase				):  # noqa: B007
				UpperCamelCase						=  a * a - b * b + x
				UpperCamelCase						=  2 * a * b + y
				UpperCamelCase						=  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 (      lowercase				)     ->						tuple:
		'''simple docstring'''

		if distance == 1:
				return (0, 0, 0)
		else:
				return (255, 255, 255)


def    A (      lowercase				)     ->						tuple:
		'''simple docstring'''

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


def    A (      lowercase = 800					, lowercase = 600					, lowercase = -0.6					, lowercase = 0					, lowercase = 3.2					, lowercase = 50					, lowercase = True					, )     ->						Image.Image:
		'''simple docstring'''

		UpperCamelCase						=  Image.new('RGB'					, (image_width, image_height)				)
		UpperCamelCase						=  img.load()

		# loop through the image-coordinates
		for image_x in range(lowercase				):
				for image_y in range(lowercase				):
						# determine the figure-coordinates based on the image-coordinates
						UpperCamelCase						=  figure_width / image_width * image_height
						UpperCamelCase						=  figure_center_x + (image_x / image_width - 0.5) * figure_width
						UpperCamelCase						=  figure_center_y + (image_y / image_height - 0.5) * figure_height

						UpperCamelCase						=  get_distance(lowercase					, lowercase					, lowercase				)

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

		return img


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# colored version, full figure
					_UpperCAmelCase      :				List[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()


from string import ascii_uppercase

_UpperCAmelCase      :				Dict          = {char: i for i, char in enumerate(ascii_uppercase)}
_UpperCAmelCase      :				Tuple          = dict(enumerate(ascii_uppercase))


def    A (      lowercase					, lowercase				)     ->						str:
		'''simple docstring'''

		UpperCamelCase						=  len(lowercase				)
		UpperCamelCase						=  0
		while True:
				if x == i:
						UpperCamelCase						=  0
				if len(lowercase				) == len(lowercase				):
						break
				key += key[i]
				i += 1
		return key


def    A (      lowercase					, lowercase				)     ->						str:
		'''simple docstring'''

		UpperCamelCase						=  ''
		UpperCamelCase						=  0
		for letter in message:
				if letter == " ":
						cipher_text += " "
				else:
						UpperCamelCase						=  (dicta[letter] - dicta[key_new[i]]) % 26
						i += 1
						cipher_text += dicta[x]
		return cipher_text


def    A (      lowercase					, lowercase				)     ->						str:
		'''simple docstring'''

		UpperCamelCase						=  ''
		UpperCamelCase						=  0
		for letter in cipher_text:
				if letter == " ":
						or_txt += " "
				else:
						UpperCamelCase						=  (dicta[letter] + dicta[key_new[i]] + 26) % 26
						i += 1
						or_txt += dicta[x]
		return or_txt


def    A (      )     ->						None:
		'''simple docstring'''

		UpperCamelCase						=  'THE GERMAN ATTACK'
		UpperCamelCase						=  'SECRET'
		UpperCamelCase						=  generate_key(lowercase					, lowercase				)
		UpperCamelCase						=  cipher_text(lowercase					, lowercase				)
		print(f'''Encrypted Text = {s}'''				)
		print(f'''Original Text = {original_text(lowercase					, lowercase				)}'''				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()
