The disclosure provides an approach for approximating a fully calculated image sequence from a subset of calculated image data. In one configuration, a rendering application calculates, for each image in the image sequence, a subset of pixels including pixels previously occluded by object(s) in preceding images and pixels whose ages have exceeded a threshold value. The rendering application then approximates the remaining non-calculated image data by interpolating the image data that has been calculated and merges the calculated and approximated image data to obtain the final image sequence. In a particular configuration, entire images may be recalculated at regular intervals to prevent excessive image quality degradation. In another configuration, the recalculation of pixel data may be offset by randomly initializing pixel age values. In yet another configuration, a combination of recalculating entire images and refreshing pixels at offset intervals may be used.