# Laplacian Operator with and without Diagonal Direction Elements in the Kernel

This is a general question on the laplacian operator, which has two different versions. The first version is :

\begin{matrix} 0 & 1 & 0 \\ 1 & -4 & 1 \\ 0 & 1 & 0 \end{matrix}

The second version includes the diagonal:

\begin{matrix} 1 & 1 & 1 \\ 1 & -8 &1 \\ 1 & 1 & 1 \end{matrix} Including the diagonal direction will make the laplacian isotropic. But what exactly is isotropic? How would that affect the resulting image if the diagonal components are included? What happen if I don't include the diagonal components?