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This strange plant appeared to trap insect in each individual "flower pit". I need to know more about this.
With leaf damage. The plant is very common around here, often with lots of leaf damage similar to this.
Piperales is a botanical name for an order of flowering plants. It necessarily includes the family Piperaceae but otherwise has been treated variously over time. Well-known plants which may be included in this order include black pepper, kava, lizard's tail, birthwort, and wild ginger.