The beauty of the creature is nothing other than the likeness of divine beauty participated in things.
(I'm pretty sure it comes from his commentary on Ps. Dionysius' On the Divine Names, but I don't have the reference handy.)
Its the phrase 'participated in things' that I find particularly interesting. Of course, being the consistent thinker he was, and astute student of his tradition, he would say equivalent things about the being of things and the goodness of things. Remember, there are considered to be three so-called 'transcendentals' - truth, beauty and goodness - and with each of them there is connoted some sort of resemblance of creatures to God. (And Christians know that these are convertible notions, since they are really 'about' God and God is 'simple' (He has no parts)). So in speaking of the goodness of things, Thomas says something about things moving with the movement of God, and of the truth of things, that they are God's ideas of these things as actual; I recall that he even states it more dramatically that things are God's ideas of those things as if He were himself those things. My dastardly paraphrasing. The point is in this case, that these things share His existence, and must draw on the divine resource somehow, which is being only, nothing else. So participated, whether we mean participating in the beauty, goodness, or truth of God, means the specific way in which a thing's particularity is a unique representation of something about God.
We can conclude from this that
- every type of thing is intended by God as a reflection of Himself for which nothing else can substitute.
- every individual thing is intended by God as a reflection of Himself for which nothing else can substitute.
Thomas, then, would agree that no two snowflakes are alike, but he would go one step further. No two anything are exactly alike, he would say, yet all things are like God but in unlike manners.
What is beauty? Likeness to God. What is that? Something that delights the mind, the heart, the body in a total, unalloyed manner.