


'''simple docstring'''

import colorsys

from PIL import Image  # type: ignore

def _SCREAMING_SNAKE_CASE (A    ,					A    ,					A			)			->			float:






       """simple docstring"""







       lowercase__      =					x
       lowercase__      =					y
       for step in range(A			):  # noqa: B007
              lowercase__      =					a * a - b * b + x
              lowercase__      =					2 * a * b + y
              lowercase__      =					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 _SCREAMING_SNAKE_CASE (A			)			->			tuple:






       """simple docstring"""







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

def _SCREAMING_SNAKE_CASE (A			)			->			tuple:






       """simple docstring"""







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

def _SCREAMING_SNAKE_CASE (A = 800    ,					A = 600    ,					A = -0.6    ,					A = 0    ,					A = 3.2    ,					A = 50    ,					A = True    ,					)			->			Image.Image:






       """simple docstring"""







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

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

                     lowercase__      =					get_distance(A    ,					A    ,					A			)

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

       return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 lowerCamelCase				:  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'''

def _SCREAMING_SNAKE_CASE (A    ,					A    ,					A			)			->			list:






       """simple docstring"""







       lowercase__      =					len(A			)
       lowercase__      =					[[0] * n for i in range(A			)]
       for i in range(A			):
              lowercase__      =					y_points[i]

       for i in range(2    ,					A			):
              for j in range(A    ,					A			):
                     lowercase__      =					(
                         (xa - x_points[j - i + 1]) * q[j][i - 1]
                         - (xa - x_points[j]) * q[j - 1][i - 1]
                     ) / (x_points[j] - x_points[j - i + 1])

       return [q[n - 1][n - 1], q]


if __name__ == "__main__":
 import doctest

 doctest.testmod()




