




import colorsys

from PIL import Image  # type: ignore




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase ):
				__magic_name__						:						Any										=x
				__magic_name__						:						Dict										=y
				for step in range(lowerCamelCase ):  # noqa: B007
								__magic_name__						:						str										=a * a - b * b + x
								__magic_name__						:						int										=2 * a * b + y
								__magic_name__						:						Union[str, 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_ (						lowerCamelCase ):
				if distance == 1:
								return (0, 0, 0)
				else:
								return (255, 255, 255)




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




def 		lowerCAmelCase_ (						lowerCamelCase = 800						,  lowerCamelCase = 600						,  lowerCamelCase = -0.6						,  lowerCamelCase = 0						,  lowerCamelCase = 3.2						,  lowerCamelCase = 50						,  lowerCamelCase = True						,  ):
				__magic_name__						:						Tuple										=Image.new("""RGB"""						,  (image_width, image_height) )
				__magic_name__						:						List[Any]										=img.load()

				# loop through the image-coordinates
				for image_x in range(lowerCamelCase ):
								for image_y in range(lowerCamelCase ):
												# determine the figure-coordinates based on the image-coordinates
												__magic_name__						:						Optional[int]										=figure_width / image_width * image_height
												__magic_name__						:						Optional[int]										=figure_center_x + (image_x / image_width - 0.5) * figure_width
												__magic_name__						:						Tuple										=figure_center_y + (image_y / image_height - 0.5) * figure_height

												__magic_name__						:						Optional[int]										=get_distance(lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase )

												# color the corresponding pixel based on the selected coloring-function
												if use_distance_color_coding:
																__magic_name__						:						Optional[int]										=get_color_coded_rgb(lowerCamelCase )
												else:
																__magic_name__						:						int										=get_black_and_white_rgb(lowerCamelCase )

				return img


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							# colored version, full figure
							UpperCAmelCase_		:					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 __future__ import annotations

from PIL import Image

# Define glider example
__a   :							Tuple						= [
    [0, 1, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0, 0],
    [1, 1, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
]

# Define blinker example
__a   :							Optional[Any]						= [[0, 1, 0], [0, 1, 0], [0, 1, 0]]



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      list[list[int]]     )    ->   list[list[int]]:





    """simple docstring"""

    __A       =						[]
    for i in range(len(__lowercase     )     ):
        __A       =						[]
        for j in range(len(cells[i]     )     ):
            # Get the number of live neighbours
            __A       =						0
            if i > 0 and j > 0:
                neighbour_count += cells[i - 1][j - 1]
            if i > 0:
                neighbour_count += cells[i - 1][j]
            if i > 0 and j < len(cells[i]     ) - 1:
                neighbour_count += cells[i - 1][j + 1]
            if j > 0:
                neighbour_count += cells[i][j - 1]
            if j < len(cells[i]     ) - 1:
                neighbour_count += cells[i][j + 1]
            if i < len(__lowercase     ) - 1 and j > 0:
                neighbour_count += cells[i + 1][j - 1]
            if i < len(__lowercase     ) - 1:
                neighbour_count += cells[i + 1][j]
            if i < len(__lowercase     ) - 1 and j < len(cells[i]     ) - 1:
                neighbour_count += cells[i + 1][j + 1]

            # Rules of the game of life (excerpt from Wikipedia):
            # 1. Any live cell with two or three live neighbours survives.
            # 2. Any dead cell with three live neighbours becomes a live cell.
            # 3. All other live cells die in the next generation.
            #    Similarly, all other dead cells stay dead.
            __A       =						cells[i][j] == 1
            if (
                (alive and 2 <= neighbour_count <= 3)
                or not alive
                and neighbour_count == 3
            ):
                next_generation_row.append(1     )
            else:
                next_generation_row.append(0     )

        next_generation.append(__lowercase     )
    return next_generation



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      list[list[int]]      ,					__lowercase :      int     )    ->   list[Image.Image]:





    """simple docstring"""

    __A       =						[]
    for _ in range(__lowercase     ):
        # Create output image
        __A       =						Image.new("""RGB"""      ,					(len(cells[0]     ), len(__lowercase     ))     )
        __A       =						img.load()

        # Save cells to image
        for x in range(len(__lowercase     )     ):
            for y in range(len(cells[0]     )     ):
                __A       =						2_5_5 - cells[y][x] * 2_5_5
                __A       =						(colour, colour, colour)

        # Save image
        images.append(__lowercase     )
        __A       =						new_generation(__lowercase     )
    return images


if __name__ == "__main__":
  __a   :							Optional[int]						= generate_images(GLIDER, 16)
  images[0].save("out.gif", save_all=True, append_images=images[1:])




