In composition there is a rule of thirds, in which a square or rectangle is visually divided into a three by three grid and objects placed along the grid lines for balance. Balance is key with threes. A tripod balances more easily than an object with two legs or with four. Philosophically we have a kind of threes balance in democracy - two makes a majority decision in a group of three. Some religions use three manifestations of a deity. We love the story of Goldilocks and the Three Bears because we identify with the small-medium-large, the soft-comfy-hard and the two extremes of hot and cold and the "just right" in between.
Nature abounds with groups of three in the plant kingdom, so many beautiful flower and leaf structures. Google images delights me with inspiration. Here's a quilt from the archives called the Napster.
I have a lot more ideas on groups of three for tiny quilts, but it's been way too hot to sit with fabric in my lap.