# Appendix A

## Laplace Operator[^khan-1]

It is defined as $\nabla \cdot \nabla f \in \R$ and is equivalent to the
**divergence of the function**. Technically speaking it gives us the
**magnitude of a local maximum or minimum**.

Positive values mean that we are around a local maximum and vice-versa. The
higher the magnitude, the higher (or lower) is the local maximum (or minimum).

Another way to see this is as the divergence of the function that tells us whether
that is a point of attraction or divergence.

It can also be used to compute the net flow of particles in that region of space

> [!CAUTION]
> This is not a **discrete laplace operator**, which is instead a **matrix** here,
> as there are many other formulations.

[^khan-1]: [Khan Academy | Laplace Intuition | 9th November 2025](https://www.youtube.com/watch?v=EW08rD-GFh0)

