I'm having difficulty imagining (or explaining to myself) how the partial sums a two dimensional Gaussian noise can produce a surface. According to equation (20) of the paper, "On two-dimensional fractional Brownian motion and fractional Brownian random field" by Qian et.al. "the two-dimensional fractional Brownian random field is defined as a partial sum of the two dimensional fGn

$B_{h,k} = \sum_{i = 1}^h \sum_{j = 1}^k X_{i,j}$

In light of this relation, is it I am correct to say that

$B_{3,2} = X_{1,1} + X_{1,2} + X_{2,1} + X_{2,2} + X_{3,1} + X_{3,2}$

Would $B_{3,2}$ be the height of the field at $(3,2)$? ... And if the $X_{(i,.)}$s are (random) steps taken in the x-direction and the $X_{(.,j)}$s are steps in the y-direction, is it correct to add them?

I understand the concept of a random walk but the extension beyond one dimension baffles me.