dc transport through one- and two-dimensional periodic modulations of density has been investigated near half filling of the lowest Landau level. For both geometries, the modulation, which is rather weak for electrons at small magnetic fields, triggers an unexpectedly strong response for composite fermions. The dramatic effect observed in 1D gratings is best described as a large positive magnetoresistance emanating from the half filled state. 2D gratings display four peaks similar to dimensional resonances observed in antidot arrays despite the small modulation amplitude.