I want to visualize a 2D vector field, e.g.,

```
Table(Exp(-(x^2 + y^2)/4) {y, -x}, {x, -3, 3, 0.2}, {y, -3, 3, 0.2})
```

in a way where the arrow length denotes the vector length and the background color indicates the local vector orientation. Just something like the following. How can one achieve this in Mathematica?