Mathematicians Uncover Soft Cells, a New Class of Shapes in Nature

Recent mathematical research has unveiled a fascinating new class of shapes known as "soft cells." These shapes, characterised by their rounded corners and pointed tips, have been identified as prevalent throughout nature, from the intricate chambers of nautilus shells to the way seeds arrange themselves within plants. This groundbreaking work delves into the principles of tiling, which explores how various shapes can tessellate on a flat surface.

Innovative Tiling with Rounded Corners

Mathematicians, including Gábor Domokos from the Budapest University of Technology and Economics, have examined how rounding the corners of polygonal tiles can lead to innovative forms that can fill space without gaps. Traditionally, it has been understood that only specific polygonal shapes, like squares and hexagons, can tessellate perfectly. However, the introduction of "cusp shapes," which have tangential edges that meet at points, opens up new possibilities for creating space-filling tilings, highlights a new report by Nature. 

Transforming Shapes into Soft Cells

The research team developed an algorithm that transforms conventional geometric shapes into soft cells, exploring both two-dimensional and three-dimensional forms. In two dimensions, at least two corners must be deformed to create a proper soft cell. In contrast, the three-dimensional shapes can surprise researchers by completely lacking corners, instead adopting smooth, flowing contours.

Soft Cells in Nature

Domokos and his colleagues have noticed these soft cells in various natural formations, including the cross-sections of onions and the layered structures found in biological tissues. They theorise that nature tends to favour these rounded forms to minimise structural weaknesses that sharp corners might introduce.

Implications for Architecture

This study not only sheds light on the shapes found in nature but also suggests that architects, such as the renowned Zaha Hadid, have intuitively employed these soft cell designs in their structures. The mathematical principles discovered could lead to innovative architectural designs that prioritise aesthetic appeal and structural integrity.

Conclusion

By bridging the gap between mathematics and the natural world, this research opens avenues for further exploration into how these soft cells could influence various fields, from biology to architecture.