Mathematicians Uncovered A New Class Of Shape Known As Soft Cells, Which Have Been Present In Nature Long Before Humans Even Knew About Them
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.
barneyboogles – stock.adobe.com – illustrative purposes only
The softest cells were shaped almost like a saddle, with curved wing-like flaps that stretched outward.
The team speculates that any pattern of tiling that consists of regular straight-edged polyhedrons can be made softer, although they have not proven this idea to be true yet.
Soft cells could tell scientists more about biology. For instance, they could provide insights into tip growth, a type of cell expansion that is widespread in nature, particularly in algae and fungi. They could also explain why nature prefers some patterns over others.
The absence of straight edges and sharp corners in nature may be a way of conserving energy, as natural forces like elasticity and surface tension end up smoothing out corners automatically. Soft cells are everywhere in the world if you know how to look for them.
“The lack of sharp corners and their soft, highly curved geometry makes soft cells ideal candidate models for biological structures which evolved under full or partial constraint to fill space,” concluded the research team.
The study was published in the journal PNAS Nexus.
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