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Patterns In The Sand

Mother Nature may be the world’s greatest mathematician.

Bonni Kealy saw that firsthand in how tiger bush will grow in patterns found throughout other parts of nature, like the spots on a cat.

Tiger Bush in Sierra de la Gessa, Spain. Creative Commons Flickr photo courtesy of Jorge Franganillo,

“Math isn’t just about equations,” Kealy said. “It’s beautiful and natural. You see it around you every day.”

Indeed, mathematicians often tease out the numerical underpinnings of seemingly random phenomena, discerning patterns in everything from the coats of felines to algae-filled water, Kealy said. In effect, two dissimilar things are interacting in predictable ways, and a mathematician can describe how.

Kealy, 29, and her advisor David Wollkind started to create a new modeling equation for the spread of tiger bush, a plant unique to arid and semi-arid areas, by mining the past, Kealy said.

They used existing pattern formulas as a foundation for their work, but the earlier models worked only on sloped land. Kealy and Wollkind’s model works on flat land, a more common habitat for tiger bush. It focuses on how water spreads over the soil surface and interacts with plants as vegetation expires.

Kealy and Wollkind refined their formula and presented it at the Joint Mathematics Meetings earlier this year in Boston. They received so many invitations to speak at the conference that they had to turn down a few opportunities.

“The work has kind of taken on a life of its own and grown,” Kealy said. “The Joint Mathematics Meetings is kind of the Big Kahuna of math research, so we are getting some recognition.”

The work also has practical implications beyond the simple beauty of math. The equation has joined an ongoing discussion on stopping desertification, the expansion of desert landscapes.

“The big picture is to help understand this vegetation in arid climates and prevent any further desertification,” she said. “That and to show that when math works, it’s really cool.”

According to the International Fund for Agricultural Development, one-fourth of the earth is already desertified. An additional 12 million hectares are lost each year to soil degradation. This equates to losses of $42 billion in income from agriculture and other lost infrastructure.

Kealy thinks her and Wollkind’s equation can help, but she still sees room for improvement. She hopes to adjust the equation for new variables, like how water moves below the soil surface.

“This whole thing seems a little surreal,” Kealy said. “You can’t beat the chance to see your own math in action.”