Grid-08, as with a few of the gridz we've seen so far, uses repetition over a diagonal axis. In this case half of the elements in the piece are duplicated and rotated 180-degrees.
Grid-07 is composed of 5 shapes reflected over diagonal axis. Two of these shapes have more than 4 sides and are more complex than most of the shapes used in previous gridz.
Grid-4 consists of only two objects that repeat four times and create "residual" shapes in overlapping and connecting areas. These two objects are (1) a 3-spike object on each corner (can you see it?), and (2) a square that appears inside a large triangular shape four times.