In a study published in the Journal of the Royal Society Interface, scientists from the Lyon Geology Laboratory and the University of Oxford propose a theoretical model describing the formation of fractal-appearing spines in certain gastropods. This growth dynamic, although revealed in a mollusk, would also apply to many structures from the plant, fungal, and animal kingdoms.
Some gastropod shells are adorned with spiny structures exhibiting fractal-like complexity (in the mathematical sense, where details repeat at all scales). These ornaments, long enigmatic, now find an explanation through a physical model coupling mechanical instability and sequential growth.
Hierarchical patterns in various structures across plants, fungi, and animals.
The scientists show that the fractal spines of gastropod shells form when a mechanical instability of the secretory membrane episodically expands a mechanically generated self-similar pattern of micro-folds. During growth, this transformation leaves spiral striations on the shell.