Nutational sononasty is a fascinating phenomenon in plants where they exhibit rhythmic, non-directional movements in response to environmental stimuli. If you're looking to showcase this captivating behavior in outdoor plant boxes, certain plants are particularly effective.

1. Mimosa pudica (Sensitive Plant): Known for its rapid leaf-folding response to touch, this plant is a classic example of nutational sononasty. Its delicate movements make it a standout in any outdoor plant box.

2. Oxalis (Wood Sorrel): This plant displays rhythmic leaf movements, opening during the day and closing at night, making it perfect for observing nutational sononasty.

3. Phaseolus vulgaris (Common Bean): Bean plants exhibit nutational movements as their tendrils search for support, creating a dynamic display in plant boxes.

4. Dionaea muscipula (Venus Flytrap): While famous for its snapping traps, it also shows subtle nutational movements when sensing prey.

5. Passiflora (Passion Flower): Its tendrils perform slow, nutational movements as they seek climbing support, adding elegance to outdoor setups.

To optimize these plants for nutational sononasty, ensure they receive adequate sunlight, water, and space to move freely. Observing these plants can provide endless fascination and a deeper appreciation for plant behavior.