An incremental-growth model is described for the deposition of thin dielectric films with spatially modulated columnar nanostructures. Expressions, relating the ratio of the peak-to-peak modulation depth and the spatial wavelength or pitch to extreme deposition angles, are listed for the special cases of sinusoidal modulations in the deposition plane and helical columns that grow normal to the substrate. The deposition of a nanostructure modulated perpendicular to the deposition plane is, as well, demonstrated. In each case simulations made using the model display features that are similar to those shown in scanning electron microscope photographs recorded for fractures in appropriate planes.