Answer:

The pattern is adding the next odd number of squares each time—1 + 3 gives the second frame of 4, and 4 + 5 gives the third frame of 9, and 9 + 7 gives the fourth frame of 16 squares; or, the pattern is the frame number multiplied by itself—1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, and 4 x 4 = 16.