



"""simple docstring"""

import colorsys

from PIL import Image  # type: ignore




def __lowercase    (							_a	,    _a	,    _a					):
    snake_case_				:  List[str]       =			x
    snake_case_				:  Tuple       =			y
    for step in range(_a					):  # noqa: B007
        snake_case_				:  Tuple       =			a * a - b * b + x
        snake_case_				:  Dict       =			2 * a * b + y
        snake_case_				:  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 __lowercase    (							_a					):
    if distance == 1:
        return (0, 0, 0)
    else:
        return (255, 255, 255)




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




def __lowercase    (							_a = 800	,    _a = 600	,    _a = -0.6	,    _a = 0	,    _a = 3.2	,    _a = 50	,    _a = True	,    ):
    snake_case_				:  Tuple       =			Image.new('''RGB'''	,    (image_width, image_height)					)
    snake_case_				:  Union[str, Any]       =			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
            snake_case_				:  Tuple       =			figure_width / image_width * image_height
            snake_case_				:  Tuple       =			figure_center_x + (image_x / image_width - 0.5) * figure_width
            snake_case_				:  Optional[Any]       =			figure_center_y + (image_y / image_height - 0.5) * figure_height

            snake_case_				:  Dict       =			get_distance(_a	,    _a	,    _a					)

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

    return img


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     # colored version, full figure
     lowercase__					:						List[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()










"""simple docstring"""

lowercase__					:						Union[str, Any]												=			{
    '''Pillow''': '''Pillow''',
    '''accelerate''': '''accelerate>=0.11.0''',
    '''compel''': '''compel==0.1.8''',
    '''black''': '''black~=23.1''',
    '''datasets''': '''datasets''',
    '''filelock''': '''filelock''',
    '''flax''': '''flax>=0.4.1''',
    '''hf-doc-builder''': '''hf-doc-builder>=0.3.0''',
    '''huggingface-hub''': '''huggingface-hub>=0.13.2''',
    '''requests-mock''': '''requests-mock==1.10.0''',
    '''importlib_metadata''': '''importlib_metadata''',
    '''invisible-watermark''': '''invisible-watermark''',
    '''isort''': '''isort>=5.5.4''',
    '''jax''': '''jax>=0.2.8,!=0.3.2''',
    '''jaxlib''': '''jaxlib>=0.1.65''',
    '''Jinja2''': '''Jinja2''',
    '''k-diffusion''': '''k-diffusion>=0.0.12''',
    '''torchsde''': '''torchsde''',
    '''note_seq''': '''note_seq''',
    '''librosa''': '''librosa''',
    '''numpy''': '''numpy''',
    '''omegaconf''': '''omegaconf''',
    '''parameterized''': '''parameterized''',
    '''protobuf''': '''protobuf>=3.20.3,<4''',
    '''pytest''': '''pytest''',
    '''pytest-timeout''': '''pytest-timeout''',
    '''pytest-xdist''': '''pytest-xdist''',
    '''ruff''': '''ruff>=0.0.241''',
    '''safetensors''': '''safetensors''',
    '''sentencepiece''': '''sentencepiece>=0.1.91,!=0.1.92''',
    '''scipy''': '''scipy''',
    '''onnx''': '''onnx''',
    '''regex''': '''regex!=2019.12.17''',
    '''requests''': '''requests''',
    '''tensorboard''': '''tensorboard''',
    '''torch''': '''torch>=1.4''',
    '''torchvision''': '''torchvision''',
    '''transformers''': '''transformers>=4.25.1''',
    '''urllib3''': '''urllib3<=2.0.0''',
}





