GFKT

GFKT is a visualizer for generating Kepler Triangles and through their special arrangement obatining Logarithmic Spirals.

Getting Started

To start visualizing these plots on your system, follow these steps.

Clone or download the repository, then once inside the main GFKT folder run,

python3 -m pip install -r requirements.txt

You will need to install other components of manim separately, to do this visit their repository

Plotting

GFKT uses 2 libraries to plot which are matplotlib and manimlib.

To start plotting cd into src folder and execute the command,

python3 main.py

By default the plotting library is matplotlib, to use manim you can specify -manim command line argument.

For just obtaining results you can specify -noplot command line argument.

Test run with -noplot

~/GFKT/src$ python3 main.py -noplot
Enter x1, y1, f(0) & f(1)	0 0 3 4
Enter the number of points	150
{
    "lines": {
        "comment": "Converged at expected values",
        "Angle Factor": 90.0,
        "Satisfaction Factor": 0,
        "iteration": 35
    },
    "triangles": {
        "comment": "Converged to similarity between triangles",
        "factor": 1.272019649514069,
        "iteration": 36
    },
    "logarithmicSpiral": {
        "comment": "Converged at expected values",
        "a": 2.7035313754910306,
        "k": 0.1531744812651672,
        "iteration": 118
    }
}

If you want a plot, the program will ask you for the number of points to plot.

Poltting with matplotlib

It will generate a standard plot.

You can use your mouse wheel to directly zoom in/out of the plot.

Plotting with manim

To get a 480p video for the plot, just run the file as is, but to get a 1080p video remove the -pl option in main.py file at the bottom.

It will generate a video similar to this gif.(Recommended to plot 10 ~ 20 points)

Acknowledgements

tacaswell for zoomFactory.py - adds zooming properties to matplotlib plots.