cross-posted from: https://lemmy.ca/post/73190146

not open access :(, hopefully it will become open access at some point or someone will publish similar research!

Changing the values of two of the three elements in the growth law produces markedly different shells. The starting curve at the growing edge of the shell sets the shape of the shell’s opening, while the scaling factor, which the researchers call lambda (λ), determines how fast the shell expands. By changing those two factors in the model, Bhattacharya and Liu were able to generate the shape of nearly all known molluscan shells.

If only someone had a time machine to whisper this truth in the ear of Italo Calvino before he wrote his Cosmicomics series of stories!!

quote from paper abstract https://www.pnas.org/doi/10.1073/pnas.2614478123

We are guided by two principles in the spirit of D’Arcy Thompson. First, the growth is governed by the repeated and continuous application of a fixed growth law, even as the shell evolves in overall shape, without any complex biological machinery to monitor and control the growth. Second, the growth law depends solely on local geometry at the shell’s growing edge. The first principle naturally leads to the mathematical statement that the shape of the shell is generated by the action of a Lie group on a protoconch [fuckin duh bruh]. The second naturally leads to a particular representation of the Lie group. We use this representation to show that the shapes of nearly all known molluscan shells can be described by essentially three parameters: a scalar (scaling), a vector (orientation), and a curve (edge of the protoconch). We relate these parameters to the phylogenetic tree. In addition to the morphogenetic insight, our results potentially point to a alternative growth-based approach to engineering complex structures.

Wow what a strikingly beautiful thing, it is also the tiniest microdose of haunting for me because I distinctly remember remarking to a geology professor in college that I wondered if you could do a fourier transform or some kind of mathematical analysis of shells to determine if there was unifying patterns that hinted at mechanisms in some productive way and he responded with something along the lines of “but why?? what would that answer?” and all I could do was shrug and say “I have no idea, I was just wondering.”

also see https://www.caltech.edu/about/news/the-mathematics-of-growing-a-shell

paper on related subject from 2019, some great graphics https://arxiv.org/html/1901.00497v3

We note that previous work by some of the authors [36] already has highlighted the role of a spatial variation in material properties in shaping the sharp spines seen on the shells of bivalves, cephalopods and gastropods. The present communication adds to this emerging picture of the influence of physics, by shifting the focus to geometry, which, driven by morphoelastic growth, acts through the mechanism of surface growth and a parametric dependence on curvature.

Of particular interest is the further coupling of this framework with pattern formation by a range of reaction-transport equations. This would make accessible well-studied developmental milestones such as the patterning and morphogenesis of limbs and digits. Other problems in morphogenesis, such as the formation of skeletons are also within reach of our computational framework. Finally, we note that we have modelled antimarginal ornamentation events via bursts of growth. It is more likely that the growth rate does not change significantly at the location of ornamentations, but rather that the thickness of the mantle decreases, creating an increase in the length of the active mantle strip and a corresponding decrease in stiffness without requiring a strong increase in material. This effect would be interesting to incorporate in future studies, as the decrease in stiffness would further amplify the amplitudes of transverse deformation, and also may be non-uniform along the length of the mantle strip.

^ this is basically what the linked article/paper claims to have described