The geometry of Nature’s stingers is universal due to stochastic mechanical wear

Abstract

Despite their ubiquity in Nature, spikes or stingers rarely exhibit sharp tips. Instead, a closer inspection of their roughly conical tips reveals a striking similarity in their profiles: They adhere to a power-law, z ∼ r n , where n ≈ 2 . This conformity persists across diverse spatial scales and materials. The mechanistic basis for this universality was recently attributed to evolutionary selection for ease of piercing [H. Quan et al ., Proc. Natl. Acad. Sci. U.S.A. 121 , e2316320121 (2024)]. However, the transient nature of their morphology, progressively modified by repeated use and inevitable wear, has received little scrutiny. In this work, we combine tabletop experiments with continuum analysis to demonstrate that the universal tip morphology can result from stochastic weathering processes. This finding is particularly significant in light of recent observations of the same tip geometry on dissolving or melting solids and geomorphic structures in addition to biological stingers. Our results suggest that the prevalence of this power-law profile may not be the result of evolutionary selection, but rather an inevitable consequence of exposure to random erosive processes.