This is a simple python project that allows you to view fractals. It also provides a base for drawing custom fractals using the fragment shader.

This project uses NumPy, Pygame and PyOpenGL. You can install these packages with pip:

pip install numpy pygame pyopengl

Start the program by running the following command:

python fractal_viewer.py

A Pygame window should appear. You can use the Arrow Keys to move around and the [W,S] keys to zoom in/out.

1. The Pygame window is created.
2. A quad is drawn over the entire viewing area.
3. Every frame, the fragment shader is used to draw the fractal on the quad.

You can control the number of iterations that the fractal calculation will execute for by configuring the variables at the top of the fractal_viewer.py file.

If you want to simply change the number of iterations, you can do so by changing the following variable:

DEFAULT_ITERATIONS = 500

Alternatively the program can automatically determine the iteration count for a given depth. This allows for continuous zooming on the fractal without loss of quality.

WARNING: This mode can cause significant performance drops.

To minimize its effect, I have provided the ability to set the minimum and maximum number of iterations that the calculation will perform:

AUTO_UPDATE_ITERATIONS = False # Set to True for near-infinite zoom.

MIN_ITERATIONS = 1
MAX_ITERATIONS = 1000 # Set this math.inf to functionally remove the constraint. 

If you want to further adjust the iteration count in this mode, you can write your own formula to calculate the number of iterations inside the getIterationCount() function.

You can adjust the camera properties, such as the pan or zoom speed on the Camera class inside the camera.py script.

def __init__():
    ...
    self.movementSpeed = 0.3 # Pan speed.
    ...

def move():
    ...
    # Zoom in/out speed. Don't use large values.
    if keys[pg.K_w]: self.scale *=  0.999
    if keys[pg.K_s]: self.scale *=  1.001
    ...

Before you can create your own fractals, you should familiarize yourself with the way shaders work and communicate with the main program. You will probably not be interacting with the vertex.shader file at all, but you need to understand how the fragment.shader functions. You can read up on fragment shaders here.

After you do that, you should have no problem editing the fragment.shader file to draw your own fractals. Simply replace the sample mandelbrot() function with one of your own.

The fragment shader should output a vec4 variable which represents a color value, so you have to use the value returned from the fractal function to get a color. The getPointColor() function does just that.

Distributed under the MIT License. See LICENSE.md for details.

The Art of Code

The Cherno Project

The Book of Shaders

Coding Game - Adding colors to the Mandelbrot Set