Lyapunov fractals

This is a simple python project to render lyapunov fractals. It relies on numba cuda kernels that run on the gpu 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, the right mouse button to dezoom and tab to cycle through the z values of the fractal. To show the current coordinates, press space.

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.
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 class main method 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.