This repository contains Python scripts for generating fractal images using Iterated Function Systems (IFS) with customizable configurations. The scripts utilize PyTorch for computations, allowing for GPU acceleration.

• examples.py: Demonstrates how to generate fractals using predefined configurations.
• fractal_config.py: Contains definitions for various fractal configurations.
• gen_ifs_fractal.py: Defines the IFSFractal class and methods for generating and rasterizing fractals.

You can create custom fractal configurations by modifying or creating instances of FractalConfig in fractal_config.py. Each configuration requires:

• name: A unique name for the fractal.
• transformations: A list of tuples, each containing a transformation matrix and a translation vector.
• colors: A list of RGB color tuples for each transformation.
• probability_weights: (Optional) A list of probabilities for each transformation.
• activation: (Optional) The activation function to use (e.g., 'none', 'relu', 'sigmoid'). Default is 'selu'.
• batch_size: The number of points to process in each batch.
• num_iterations: The number of iterations to perform.

Example configuration:

SIERPINSKI_TRIANGLE = FractalConfig(
    name="SierpinskiTriangle",
    transformations=(
        (torch.tensor([
            [0.5, 0.0],
            [0.0, 0.5]
        ]), torch.tensor([0.0, 0.0])),
        (torch.tensor([
            [0.5, 0.0],
            [0.0, 0.5]
        ]), torch.tensor([0.5, 0.0])),
        (torch.tensor([
            [0.5, 0.0],
            [0.0, 0.5]
        ]), torch.tensor([0.25, 0.5]))
    ),
    colors=(
        (0, 127.5, 205),
        (255, 127.5, 10),
        (180, 190, 254)
    ),
    num_iterations=200000,
)

Fractal configurations can be composed easily

A_comp_B = FractalConfig(
    name="A_comp_B",
    transformations=(
        *fractal_A.transformations,
        *fractal_B.transformations
    ),
    colors=(
        *fractal_A.colors,
        *fractal_B.colors
    ),
    probability_weights=(1., 1., 8., 8., 8., 1., 1., 8.),
    activation='selu',
)

To generate fractals, you can use the generate_fractal_image function in gen_ifs_fractal.py. For example:

image = generate_fractal_image(SIERPINSKI_TRIANGLE, 
                               device='cuda', 
                               size=8192, 
                               batch_size=1000000)
image.save('sierpinski_triangle.png')

Averaging the colors of the fractal points in each iteration results in a single color for each point. The color is then mapped to a color space and the image is rasterized. I have found that HSL creates the most interesting results.

RGB

HSL