Better terrain generators will use higher-order curves rather than straight lines (i.e., instead of picking an increment for the midpoint and adding a multiple of 1 - |x|, add a multiple of 1 + cos(x)) in order to avoid having visible "corners". And of course terrain generators usually work in two dimensions, which makes this slightly more complex.

But yes, the "pick your dimensionality, randomly adjust the height in the middle, then recurse" approach is very standard.