Emily Chan
In nature, shapes mostly appear with curves and non-flat faces. It’s only through human creations that shapes with straight lines and pointed angles are common. A team of mathematicians has discovered a new class of shapes they call “soft cells.”
The shapes are capable of a geometric process called tiling without as many sharp corners. Nature has been using soft cells long before humans even knew about them.
“These shapes emerge in art, but also in biology,” said Gábor Domokos, the lead author of the study and a researcher of geometric modeling at the Budapest University of Technology and Economics.
“If you look at sections of muscle tissue, you’ll see the cells having just two sharp corners, which is one less than the triangle—it is a very special kind of tiling.”
When looked at two-dimensionally, soft cells are curved with two pinched corners known as cusps. Nautilus shells, zebra stripes, river islands, and the cross-section of onion all contain soft cell shapes.
To be characterized as a soft cell, all two-dimensional soft cells must have at least two corners that resemble teardrops and narrow to points that have an internal angle of zero degrees. But when soft cells are in three dimensions, they do not have any corners.
A two-dimensional cross-section of a nautilus shell shows shapes with two cusps and curved boundaries, but when researchers created a CT scan of the structure, they saw that the inner chamber was actually made up of three-dimensional soft cells without corners.
The team came up with an algorithm to turn regular two and three-dimensional geometric tiles into soft cells.
They measured the degree of softness that was needed for a three-dimensional space to be tiled successfully.
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