This answer contains spoilers… (view spoiler)[Earlier in the book when Frederick honorably does not throw water on the man, he is rejecting the superiors idea of the captured man, "circling the drain." I think Frederick is processing the feelings that he did not circle the drain. He survived the insults and abuse he endured at school. He is continually giving a picture of both his strength and integrity, even as he has been damaged and is unable to verbalize this. (hide spoiler)]
Pixellle First I thought the spirals was his only way of connecting to his love of birds, by describing maybe a bird in flight, or the paths that the plastic bags take as they swirl about in the wind. But then I thought about how snails' shells are also spirals, and that maybe the spirals of the snail shells and Frederick's drawings were a way to connect two good-hearted characters, two characters who walk in the light, so to speak. Also, another writer mentioned Fibonacci spiral, a golden ratio and symbol of order in the universe. Interesting.