From the intricate patterns of pollen grains to the logarithmic spirals of nautilus shells, biology is full of complex patterns, shapes, and geometries. Many of these intricate structures play important roles in biological function, but can be difficult to create in a lab without state-of-the-art equipment or expensive and energy-consuming processes and materials.

A new study describes how spheres can be transformed into twisted spindles thanks to insights from 16th century navigational tools. Researchers show how polymers can contract into spiral structures, known as loxodromes, that have complex patterning ten times smaller than the width of a human hair. Published in Physical Review Letters, the research was conducted by University of Pennsylvania graduate student Helen Ansell, postdoc Daeseok Kim, and professors Randall Kamien and Eleni Katifori in the School of Arts and Sciences, in collaboration with Teresa Lopez-Leon of the École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI).

Kim, who worked on this project at ESPCI before coming to Penn, was inspired by other studies showing that a mixture of polymer and liquid crystal took on a new shape when placed in a different solvent. It was a change that was also reversible and reproducible, with little to no energy required to cause the change in shape.