Nutational traumatronasty is a fascinating phenomenon in plants where they exhibit rapid, reversible movements in response to mechanical stimulation or touch. If you're looking to showcase this unique behavior in outdoor plant boxes, certain species are particularly effective. Here are the best plants to consider:

1. Mimosa pudica (Sensitive Plant) – Known for its rapid leaf-folding response when touched, this plant is a classic example of nutational traumatronasty. Its delicate foliage and quick reactions make it a standout choice.

2. Dionaea muscipula (Venus Flytrap) – While famous for trapping insects, this plant also demonstrates rapid movement when triggered, making it an exciting addition to any outdoor display.

3. Oxalis spp. (Wood Sorrel) – Some species of Oxalis exhibit leaf movements in response to touch or changes in light, adding dynamic visual interest to plant boxes.

4. Codariocalyx motorius (Telegraph Plant) – This plant moves its leaves in a jerky, nutational manner, especially when disturbed, making it ideal for demonstrating traumatronasty.

5. Biophytum sensitivum – Similar to Mimosa pudica, this plant reacts to touch by folding its leaves, offering another excellent option for outdoor setups.

For optimal results, ensure your plant boxes receive adequate sunlight, moisture, and protection from harsh winds. Observing these plants in action can be a rewarding experience for both gardening enthusiasts and curious onlookers. Experiment with different species to create a captivating display of nutational traumatronasty in your outdoor space.