Animation of a trefoil knot from neuron dynamics

This repository contains the necessary code to create an animation of population dynamics following a Trefoil knot.

Requirements

The exact conda environment used to create the animation can be created from the provided environment.yml file as:

conda env create -f environment.yml

This work requires the latest version of matplotlib. In fact, the latest version was modified to fix the Z-ordering problem.

matplotlib >= 3.6.1

Z-ordering problem

The standard matplotlib scripts do not correctly order the depth of lines. Thus I had to modify the latest matplotlib version to be capable of this, PR will be posted soon. In the meantime one can use the temporary fix from this fork.

Trefoil knot

I used a cartesian representation of the trefoil knot as the dynamics of the neurons:

$$ \begin{align} N_1 &= \cos{t} + 2 \cos{2t} \\ N_2 &= \sin{t} - 2 \sin{2t} \\ N_3 &= 2 \sin{3t} \end{align} $$

See this blog post for more details.

License

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International Public License.