# Hamburger Hunting

Imagine for a moment that you’re lost in the middle of nowhere. Lost, and hungry, too. You can’t remember the last time you saw a burger, and you’d be willing to fork over more than a couple dollars for a can of coke. But there isn’t any internet where you are, so you can’t simply go online to see where the nearest burger joint is. What on earth do you do?

Luckily, mathematicians have got you covered. If you’ve ever wondered what mathematicians do for a living, here it is: they find burgers. For the good of humanity.

This is what mathematicians do. Really. (Ok, not really, but you can click here for a mathematician’s opinion, or here for some talks that will give you an idea of the scope of mathematics.)

Using modelling techniques, mathematicians have found that the fastest way to find a burger – or any food for that matter – involves a bunch of short, random movements as you look for food within a small area, and then a longer hike in a random direction to a distant area, where you repeat the process. This type of search pattern is known as the Lévy walk, and is the best way to forage or hunt when food is sparsely-distributed.

But of course, the best path to take really does depend on how much food is available in the first place. When food is abundant, like when burgers are falling from the sky, it doesn’t matter how or where you move: you are bound to bump into food at some point. In this case, you can make do with Brownian motion: small random movements in any direction you like. It’s so easy that even non-living particles can do it!

This slideshow requires JavaScript.

So which strategy is most common in the animal kingdom: Brownian motion or the Lévy walk? It turns out that food isn’t as abundant as one might hope, and so the Lévy walk is generally the more efficient choice. In fact, the Lévy walk has been used for at least 50 million years by sea urchins, and today is used by a wide range of animals including albatrosses, bumblebees, deer, sharks, and even amoeba. In my independent project, I found that periwinkle snails (Littorina littorea) might also utilize the Lévy walk for foraging, although no one has showed this conclusively for snails or any of their relatives just yet.

The Hadza also perform Lévy walks when hunting and foraging.

But if you thought that Lévy walk was only applicable to animals, you’d be wrong, since patterns of Lévy walk have been found in humans, too! A study published in 2013 by David Raichlen and his colleagues showed that the Hadza people – a tribe of Tanzanian hunter-gatherers – exhibited Lévy-like search patterns when foraging.

It is also possible that you and I use the Lévy walk on a daily basis. After all, if you think about your daily routine, what is it comprised of? Most likely, periods of long-distance travel (commuting to work, school, or home), interspersed with shorter, more random movements!

Unfortunately, since the application of the Lévy walk model to optimal foraging is relatively recent, this possibility has not been well-tested. Who knows? In the future, researchers might show that all of us really are Lévy-walkers at the core. Man and animal might not be so different after all, at least when it comes to being hungry!