Nutational nastic movements are fascinating plant behaviors where stems or tendrils move in a circular or spiral motion to seek support or sunlight. If you're looking to observe these dynamic movements in outdoor plant boxes, certain plants are ideal for showcasing this phenomenon.

1. Sweet Pea (Lathyrus odoratus): Known for its delicate tendrils, sweet pea exhibits clear nutational movements as it climbs, making it perfect for plant boxes with trellises.

2. Morning Glory (Ipomoea purpurea): This fast-growing vine displays pronounced spiraling motions as it wraps around supports, creating a visually striking effect.

3. Passionflower (Passiflora spp.): With its vigorous climbing habit, passionflower demonstrates elegant nutational growth, ideal for larger outdoor boxes.

4. Hop (Humulus lupulus): A robust climber, hop plants show strong helical movements, making them a great choice for observing nastic behaviors.

5. Bean Plants (Phaseolus vulgaris): Common beans exhibit nutational movements as their stems search for support, offering an easy-to-grow option for beginners.

To enhance these movements, ensure your plant boxes have adequate support structures like stakes or mesh. Regular watering and sunlight will encourage healthy growth and more pronounced nutational patterns. Observing these plants can be both educational and aesthetically pleasing, adding a dynamic element to your garden.