
"""simple docstring"""

import colorsys

from PIL import Image  # type: ignore






def 							A		(       snake_case   :float       ,      snake_case   :float       ,      snake_case   :int	)   ->			float:
 __UpperCamelCase       						= x
 __UpperCamelCase       						= y
 for step in range(snake_case	):  # 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		(       snake_case   :float	)   ->			tuple:
 if distance == 1:
  return (0, 0, 0)
 else:
  return (2_5_5, 2_5_5, 2_5_5)






def 							A		(       snake_case   :float	)   ->			tuple:
 if distance == 1:
  return (0, 0, 0)
 else:
  return tuple(round(i * 2_5_5	) for i in colorsys.hsv_to_rgb(snake_case       ,      1       ,      1	)	)






def 							A		(       snake_case   :int = 8_0_0       ,      snake_case   :int = 6_0_0       ,      snake_case   :float = -0.6       ,      snake_case   :float = 0       ,      snake_case   :float = 3.2       ,      snake_case   :int = 5_0       ,      snake_case   :bool = True       ,      )   ->			Image.Image:
 __UpperCamelCase       						= Image.new('RGB'       ,      (image_width, image_height)	)
 __UpperCamelCase       						= 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
   __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(snake_case       ,      snake_case       ,      snake_case	)

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

 return img


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      # colored version, full figure
      UpperCamelCase			:       List[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"""

import re

from filelock import FileLock


try:
      import nltk

      UpperCamelCase			:       int									=				True
except (ImportError, ModuleNotFoundError):
      UpperCamelCase			:       List[str]									=				False

if NLTK_AVAILABLE:
      with FileLock(".lock") as lock:
            nltk.download("punkt", quiet=True)






def 							A		(       snake_case   :str	)   ->			str:
 re.sub('<n>'       ,      ''       ,      snake_case	)  # remove pegasus newline char
 assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
 return "\n".join(nltk.sent_tokenize(snake_case	)	)



