'''simple docstring'''

import colorsys

from PIL import Image  # type: ignore







def      UpperCamelCase_						(					snake_case_       :       float						,		snake_case_       :       float						,		snake_case_       :       int      )					->     float:






 '''simple docstring'''

 __lowerCAmelCase											=						x
 __lowerCAmelCase											=						y
 for step in range(snake_case_      ):  # noqa: B007
  __lowerCAmelCase											=						a * a - b * b + x
  __lowerCAmelCase											=						2 * a * b + y
  __lowerCAmelCase											=						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_						(					snake_case_       :       float      )					->     tuple:






 '''simple docstring'''

 if distance == 1:
  return (0, 0, 0)
 else:
  return (2_55, 2_55, 2_55)







def      UpperCamelCase_						(					snake_case_       :       float      )					->     tuple:






 '''simple docstring'''

 if distance == 1:
  return (0, 0, 0)
 else:
  return tuple(round(i * 2_55      ) for i in colorsys.hsv_to_rgb(snake_case_						,		1						,		1      )      )







def      UpperCamelCase_						(					snake_case_       :       int = 8_00						,		snake_case_       :       int = 6_00						,		snake_case_       :       float = -0.6						,		snake_case_       :       float = 0						,		snake_case_       :       float = 3.2						,		snake_case_       :       int = 50						,		snake_case_       :       bool = True						,		)					->     Image.Image:






 '''simple docstring'''

 __lowerCAmelCase											=						Image.new("""RGB"""						,		(image_width, image_height)      )
 __lowerCAmelCase											=						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
   __lowerCAmelCase											=						figure_width / image_width * image_height
   __lowerCAmelCase											=						figure_center_x + (image_x / image_width - 0.5) * figure_width
   __lowerCAmelCase											=						figure_center_y + (image_y / image_height - 0.5) * figure_height

   __lowerCAmelCase											=						get_distance(snake_case_						,		snake_case_						,		snake_case_      )

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

 return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 _A			:      Optional[int]					      =				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

 _A			:      int					      =				True
except (ImportError, ModuleNotFoundError):
 _A			:      Optional[Any]					      =				False

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







def      UpperCamelCase_						(					snake_case_       :       str      )					->     str:






 '''simple docstring'''

 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_      )      )






