Lyapunov fractals

This is a simple python project to render lyapunov fractals. It relies on numba cuda kernels for relatively fast fractal generation.

Requirements

• the numba package with cuda.
• numpy, pygame and pillow, that you can install with pip install numpy pygame pillow

and that's it!

Features

Image generation

Running the file generate_fractal_image.py creates an image of a fractal and displays it to the screen.

Video generation

Running the file generate_fractal_video.py creates and stores a gif cycling through slices of a 3D lyapunov fractal in the $z$ direction.

Interactive pygame window

Running the file fractal_zoom.py opens a pygame window with a fractal:

• Press the left mouse button to zoom
• Press the right mouse button to dezoom
• Press tab to cycle through the $z$ values of the fractal
• Press space to show the current coordinates.
• Press s to generate a higher resolution image of the current fractal, and press s again to save the image.
• Press c to cycle the pattern.

Details

The main class is ComputeFractals. Its parameters are the following:

• x_min, x_max, y_min, y_max, z_min, z_max define the region in which fractals will be computed. These values need to be between 0 and 4.
• size: the size of the generated images in pixels.
• colors: a list of hex colors
• color_resolution: how many different shades of the color list self.COLORS are used.
• pattern: a string of "x", "y", and "z". The pattern defines which fractal is generated.
• num_iter: defines at which precision the pixel values are computed.

These parameters can be modified after the class construction by accessing them directly, except for:

• num_iter which can not be changed.
• the $x$ and $y$ boundaries, that you can change with the set_region method.
• the pattern, that you can change with the set_pattern method.

The main method of ComputeFractals is compute_fractal(z), which computes a slice of a 3D lyapunov fractal at a given $z$ value. This parameter doesn't matter if $z$ doesn't appear in the pattern.

The class FractalZoom with the run method creates a pygame window and handles the zoom logic.