Deforming orthogonal grid geometry to an irregular one

Hey guys,

I have this regular grid geometry (shown as white cells, in the image) where I want to introduce a deformation without changing the basis of the grid creation (it works on subdivision of cells, and irregular cells were not being subdivided evenly - hence the manipulation required after achieving this result). Any quick ways of doing this, maybe based on attractor curves/points?

I know I may be missing something very fundamental here.

Thanks