The mathematics of growing a shell—recreating diverse mollusk shells with just three inputs
Kaushik Bhattacharya is an engineer and materials scientist, but he has always been fascinated by seashells. Part of the draw is the "beautiful" idea that even simple organisms like mollusks can construct wonderfully complex structures over and over again, even in differing environments. He marvels at nature's engineering capabilities.
An engineer and materials scientist, Kaushik Bhattacharya, has collaborated with Caltech professor Howell N. Tyson, Sr., and postdoctoral scholar Huan Liu to discover a mathematical method that explains how mollusk shells are formed. The researchers found that the growth of mollusk shells can be explained using just three mathematical elements: the shape at the leading edge of a developing shell (the curve element), a scaling factor that reflects how fast the shell expands, and the angle of the shell's rotation.
This mathematical approach can accurately recreate the shells of various mollusk classes, from the coiled nautilus shell to the fan-like scallop shell, using only these three elements. The shell growth process is both passive and energy efficient, as it happens without additional control and consumes minimal energy. The research, published in Proceedings of the National Academy of Sciences, could potentially be applied to create other complex materials, such as specialized manifolds for jet engines.
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- The Mathematics of Growing a Shell caltech.edu
