




import colorsys

from PIL import Image  # type: ignore







def lowerCamelCase__  (     _lowercase					,		_lowercase					,		_lowercase ):

     '''simple docstring'''


     UpperCAmelCase_     :				Union[str, Any]  =     x
     UpperCAmelCase_     :				List[str]  =     y
     for step in range(_lowercase ):  # noqa: B007
          UpperCAmelCase_     :				Union[str, Any]  =     a * a - b * b + x
          UpperCAmelCase_     :				List[Any]  =     2 * a * b + y
          UpperCAmelCase_     :				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 lowerCamelCase__  (     _lowercase ):

     '''simple docstring'''


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







def lowerCamelCase__  (     _lowercase ):

     '''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 lowerCamelCase__  (     _lowercase = 800					,		_lowercase = 600					,		_lowercase = -0.6					,		_lowercase = 0					,		_lowercase = 3.2					,		_lowercase = 50					,		_lowercase = True					,		):

     '''simple docstring'''


     UpperCAmelCase_     :				int  =     Image.new('''RGB'''					,		(image_width, image_height) )
     UpperCAmelCase_     :				List[str]  =     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_     :				str  =     figure_width / image_width * image_height
               UpperCAmelCase_     :				Dict  =     figure_center_x + (image_x / image_width - 0.5) * figure_width
               UpperCAmelCase_     :				Any  =     figure_center_y + (image_y / image_height - 0.5) * figure_height

               UpperCAmelCase_     :				int  =     get_distance(_lowercase					,		_lowercase					,		_lowercase )

               # color the corresponding pixel based on the selected coloring-function
               if use_distance_color_coding:
                    UpperCAmelCase_     :				Dict  =     get_color_coded_rgb(_lowercase )
               else:
                    UpperCAmelCase_     :				int  =     get_black_and_white_rgb(_lowercase )

     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

import math

__a							     =					'2020.9.26'
__a							     =					'xcodz-dot, cclaus, dhruvmanila'







def lowerCamelCase__  (     _lowercase					,		_lowercase					,		_lowercase					,		_lowercase					,		_lowercase ):

     '''simple docstring'''


     if not all(isinstance(_lowercase					,		(float, int) ) for val in locals().values() ):
          UpperCAmelCase_     :				Optional[int]  =     f'''Input values must either be float or int: {list(locals().values() )}'''
          raise TypeError(_lowercase )
     UpperCAmelCase_     :				Tuple  =     ((x * distance) / (z + distance)) * scale
     UpperCAmelCase_     :				str  =     ((y * distance) / (z + distance)) * scale
     return projected_x, projected_y







def lowerCamelCase__  (     _lowercase					,		_lowercase					,		_lowercase					,		_lowercase					,		_lowercase ):

     '''simple docstring'''


     if not isinstance(_lowercase					,		_lowercase ):
          raise TypeError('''Axis must be a str''' )
     UpperCAmelCase_     :				Optional[Any]  =     locals()
     del input_variables["axis"]
     if not all(isinstance(_lowercase					,		(float, int) ) for val in input_variables.values() ):
          UpperCAmelCase_     :				List[Any]  =     (
              '''Input values except axis must either be float or int: '''
              f'''{list(input_variables.values() )}'''
          )
          raise TypeError(_lowercase )
     UpperCAmelCase_     :				Dict  =     (angle % 360) / 450 * 180 / math.pi
     if axis == "z":
          UpperCAmelCase_     :				Optional[int]  =     x * math.cos(_lowercase ) - y * math.sin(_lowercase )
          UpperCAmelCase_     :				List[Any]  =     y * math.cos(_lowercase ) + x * math.sin(_lowercase )
          UpperCAmelCase_     :				Optional[int]  =     z
     elif axis == "x":
          UpperCAmelCase_     :				Any  =     y * math.cos(_lowercase ) - z * math.sin(_lowercase )
          UpperCAmelCase_     :				int  =     z * math.cos(_lowercase ) + y * math.sin(_lowercase )
          UpperCAmelCase_     :				Dict  =     x
     elif axis == "y":
          UpperCAmelCase_     :				Union[str, Any]  =     x * math.cos(_lowercase ) - z * math.sin(_lowercase )
          UpperCAmelCase_     :				Optional[int]  =     z * math.cos(_lowercase ) + x * math.sin(_lowercase )
          UpperCAmelCase_     :				Optional[int]  =     y
     else:
          raise ValueError('''not a valid axis, choose one of \'x\', \'y\', \'z\'''' )

     return new_x, new_y, new_z


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(F"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
     print(F"""{rotate(1.0, 2.0, 3.0, "y", 90.0) = }""")