848 B
848 B
Appendix A
Laplace Operator1
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.