Unlike the balanced look of even numbers, the asymmetry of odd numbers captures your attention and forces your gaze to move across the arrangement. Grouping items in threes or even other odd numbers, such as fives or sevens is a Designer go to for accents, artwork and even furniture groupings.
Though I love a symmetrical look as well, symmetry lends itself to a more traditional feel. Todays more modern looks call for asymmetry. The rule of 3 also applies to height as well. To keep the eye moving you want to have a layered look of something tall, medium and short.
The rule of 3 concept not only works with objects and furniture but extends to patterns and colors. Start with a Solid (or mini print) add in a movement pattern like a floral then finish with something geometric like a stripe or plaid. See the photo below, by using these 3 different pillows it adds visual interest to the large solid sofa.
Group three items on a table or shelve. Use complementary colors but mix variations of shape and size.
The best part of applying the rule of three is that you don’t have to totally revamp your décor. Sometimes just by removing or adding an accessory here and there, can a huge difference. Don't forget to leave some negative space between groupings. By doing this it allows your eye to rest between moments and makes them all that more special.
Have fun and don't overthink it. Cheers! - Julie