Mathematicians at the Budapest University of Technology and Economics have discovered a new class of geometric shapes that characterizes forms commonly found in nature. The shape derives its inspiration from the chambers in the iconic spiral shell of the Nautilus to how seeds pack into plants.
Humans, despite being the most intelligent creatures on Earth and knowing the superabundance of geometric shapes, are still thrilled with the enigmas of Mother Nature. Nature does the shaping and re-shaping in the most effective way possible than we humans do. For instance, if humans are asked about the use of polygons to pack together to fill 2D space with no gaps, we might end up thinking about shapes like squares, triangles, or hexagons. But nature has its own ways of proving its influentiality.
For a long time now, Mathematicians have deciphering the shape to fill the surfaces without leaving any gaps. Unlike the mathematician’s approach, the natural world embeds patterns, characterized by shapes with curved edges and non-flat faces. These complex patterns have always challenged mathematical explanations.
“A central problem of geometry is the tiling of space with simple structures. Many tilings in Nature are characterized by shapes with curved edges, nonflat faces, and few if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes.” says the new paper published at the University of Oxford.
“We solve this problem by introducing a new class of shapes, the soft cells, minimizing the number of sharp corners and filling space as soft tilings.”
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Soft Cell – a new class of mathematical shapes
These complexities are answered by a new class of mathematical shapes called Soft Cells. Soft Cells are shapes with minimal sharp corners that cover space without gaps.
In 2D, these soft cells have curved boundaries with only two corners. These are common features of muscle cells or braided rivers. Meanwhile, soft cells in the 3D space are even more complex and intriguing.
In 3D, the team showed that the shape can be softened by allowing the edges to bend whilst minimizing the number of sharp corners.
‘Nature not only abhors a vacuum, she also seems to abhor sharp corners’ explained Professor Alain Goriely.
“Soft cells help explain why, when you look at a cross-section of a chambered shell, it shows corners but the 3D geometry of the chambers doesn’t.”, says Professor Domokos.
Soft Cells appear to be the building block shapes in nature, and a new study could shed light on why certain patterns are preferred by nature.
Journal Reference:
Domokos, G., Goriely, A., & Horváth, Á. G. (2024). Soft cells and the geometry of seashells. PNAS Nexus, 3(9). https://doi.org/10.1093/pnasnexus/pgae311