Two Dimensions

In two dimensions we can plot the noise values as a density in a picture. This looks a bit like clouds or cotton wool.

The filtered noise is made in the same way by convolution but here the filter is a function of two dimensions and averages nearby points in a 2D grid.

You can think of the green circle as the filter 'footprint'. Only points within the  circle are averaged to calculate the filtered noise value at the centre.