Mathematicians have identified a new geometric shape called ‘soft cells’, which can be seen in nature’s designs—from the layers of an onion to the spiral chambers of the nautilus shell. These shapes have rounded corners and pointed tips, fitting together in ways that fill space while minimizing sharp angles. 🌿
What Are Soft Cells?
Soft cells are rounded, teardrop-like shapes with curved edges, unlike traditional polygonal tiles such as squares or hexagons. They tessellate on a surface, meaning they can fit together without leaving gaps. This is significant because nature often avoids sharp corners, which can create structural weaknesses. The theory goes that nature “softens” these corners to reduce energy costs in the process of formation. 🌊
The Mathematical Discovery 📐
Led by mathematician Gábor Domokos and his team at the Budapest University of Technology and Economics, the research presents a new algorithm that transforms polygons (2D) and polyhedra (3D) into these soft cells. In 3D, these cells can even fill volumetric space without any corners at all.
The team’s findings have implications for understanding natural formations, as they identified soft tilings in structures such as braided rivers, plant cells, and even in the iconic spiral shell of the nautilus. 🐚
How Soft Cells Fit in Nature
The research shows that many natural shapes, like the concentric layers in onions and the chambers inside spiral shells, follow this new soft-cell pattern. The work provides a fresh perspective on how nature’s designs—like those seen in molluscs, riverbanks, and biological tissues—are formed to avoid sharp angles, which can compromise structural integrity. 🌾
Domokos believes that soft cells may optimize physical forces, like reducing bending energy in edges or maximizing stability, although this theory still awaits proof.
Applications in Architecture 🏛️
Interestingly, soft cells aren’t just found in nature. The late architect Zaha Hadid intuitively employed these shapes in her designs, using curves and rounded forms to minimize sharp angles, both for aesthetic and structural reasons. Architects today are collaborating with Domokos’ team to create innovative designs that mimic the efficiency and beauty of nature’s soft cells.
This exciting discovery blends geometry with natural processes, showing us once again that math is not only about numbers, but also about understanding the world around us in new ways. 🔍