Credit: Wikimedia (CC BY-SA 4.0)Įveryone uses Voronoi tessellations, even without realizing it. A scutoid is more complicated than a prismatoid, which is more complicated than a frusta, which is more complicated than a prism. The researchers derived the word “scutoid” from the scutellum of beetle-see Figure 4–as the two share attributes. The tightly-packed, scutoid-shaped epithelial cells that line skin, intestines, blood vessels, and organs are the cells in a three-dimensional Voronoi tessellation.įigure 4. Any point inside a bubble is closer to the site of its bubble than the site of any other bubble. Imagine a box filled with bubbles-the cells-that expand to meet in planes. Three-dimensional Voronoi tessellations are constructed analogously, except the sites are scattered in 3-dimensional space and the cells around them are 3-dimensional shapes with flat sides. Bee honeycombs may be modeled with Voronoi tessellation sites that are placed in a regular pattern. The pattern in Figure 3 resembles the irregular patterns on giraffe fur and dragonfly wings as both may be modeled with Voronoi tessellations. When the kindergartener identifies some classmates he expects to run to “his” piece of candy and others he expects will run to other pieces of candy, he is drawing a mental Voronoi tessellation map. In this game, when a kindergartener scans the room and identifies the piece of candy-his site-to which he is closest, Buceta says the child is modeling the situation with a Voronoi tessellation. Credit: Jaymz Height-Field Wikimedia (CC BY-SA 3.0)Īlso, a kid on a boundary line is equidistant to candies in neighboring cells. The nonoverlapping shapes with straight sides-polygons-depict the regions in which kids may stand at the start are the tessellation’s “cells.” Any kid inside an individual cell is closer to the candy (the site) in his or her cell than candies (sites) in any other cells.įigure 3. The black dots, which depict the scattered candies, are the “sites” of the tessellation. His kindergarten Voronoi tessellation example might be illustrated with the diagram in Figure 3.
Once the candy lands, tell the kids to run to the candy that is closest to them,” said Buceta. Throw some candy in a kindergarten classroom where children are randomly playing.
#TESSELLATION EXAMPLES IN REAL LIFE HOW TO#
“Even kindergarteners know how to make Voronoi tessellations. Imagine the researchers’ surprise, however, when their microscopes revealed that scutoid-shaped epithelial cells were pervasive in the human body, news they published last July in Nature Communications.
The model indicated that epithelial cells should take the form of an unusual and previously unknown shape they named the “scutoid.” Of course, epithelial cells in nature were under no obligation to observe the model, especially as the oddly-shaped, not-previously-observed scutoid seemed like an unlikely candidate. Credit: Giuliagi Wikimedia (CC BY-SA 3.0)
#TESSELLATION EXAMPLES IN REAL LIFE SKIN#
Given Voronoi tessellations’ prevalence in nature, Buceta and his colleagues used this mathematical model to predict the shape of epithelial cells, which among other things make up the surface of your skin and the inside of your throat, intestines and blood vessels. “Many times, the patterns you see in nature are Voronoi tessellations,” says Javier Buceta, a member of a team of Spanish, British, and American researchers that recently sought to predict the shape of epithelial cells-the cells that line the surfaces of our skin, intestines, blood vessels, and organs. All these natural patterns may be modeled with a mathematical technique known as a Voronoi tessellation. And the honeycomb cells built by bees also appear to fit together, although in this case arrangement is regular. The delicate veins on a dragonfly’s wings also outline a puzzle-like collection of irregular translucent cells. Look at giraffe’s fur and you’ll see a collection of irregular brown spots that fit together like puzzle pieces.
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