Why can't you hit flies? Because they are better at math than you are

When eating outside in the summer, flies often come uninvited. Hitting flies is a technical job, because the flight trajectory of flies is very strange, and it is difficult for humans to find the target with just their hands.

So the question is, why do flies fly around?

You may not know that flies' flying around like this actually applies a powerful mathematical principle , which makes their flight path elusive and avoids being hit.

This mathematical principle is called Lévy flight . The route map of Lévy flight is as follows:

Image source: Wikipedia

Lévy flights are a type of fractal , meaning that no matter how many times you magnify them, they still look similar to the original pattern. More importantly, Lévy flights are random walks , meaning that their trajectory cannot be accurately predicted, just like the ghostly steps of a fly .

Apparently, Lévy flight helps flies avoid predators and humans who want to bash their heads in. In 2008, a team led by biologist Masakazu Shimada of the University of Tokyo discovered that the flight patterns of houseflies (Musca domestica) are examples of Lévy flight.

Not only houseflies, but also common fruit flies in the home are also Lévy flyers. For example, when Drosophila melanogaster flies, they often fly in a straight line with a mixture of rapid 90-degree turns. Their flight paths are a perfect Lévy flight diagram:

Levy flight of Drosophila melanogaster. Image source: (doi) 10.1371/journal.pone.0000354

We learned in middle school that some tiny particles will experience Brownian motion.

Brownian motion, Image source: Wikipedia

Although Brownian motion is also a random walk, Lévy flight is different from Brownian motion.

One characteristic of Brownian motion is that the length of each step is concentrated in one area , which can be plotted as a bell curve:

This is not the case with Levy flight. In the Levy flight diagram, the distance of each step conforms to the power law. In other words, in the Levy flight motion, most of the steps are short, but a few are long .

The step length of the Lévy flight is a power function

You may ask, there is a difference between Levy flight and Brownian motion, but what is the use of this?

The different nature of the step lengths of Levy flight and Brownian motion directly leads to the fact that Levy flight is more efficient than Brownian motion . With the same number of steps or distance, the displacement of Levy flight is much larger than that of Brownian motion, and it can explore a larger space.

Comparison of the efficiency of Brownian motion (left) and Levy flight (right). Obviously, Levy flight covers a larger area with less distance and steps, which is very useful for exploring the unknown. Image source: (DOI)10.1038/nature04292

This is crucial for creatures that need to explore unknown areas. As expected, Paul Pierre Lévy, the French mathematician who discovered Lévy flight and the mentor of the great Benoît B. Mandelbrot, was the first to discover that many random movements of life belong to Lévy flight, rather than Brownian motion like molecules.

For example, when sharks and other marine predators know that there is food nearby, they use Brownian motion because Brownian motion helps to "open and clear" hidden food in a small area. But when food is scarce and new territories need to be opened, marine predators will abandon Brownian motion and adopt the strategy of Levy flight .

In 2008, a team of researchers from the UK and US published a study in the journal Nature in which they attached trackers to 55 different marine predators in the Atlantic and Pacific Oceans (including silky sharks, swordfish, blue marlin, yellowfin tuna, turtles and penguins) and tracked their movements over 5,700 days.

After analyzing 12 million of their movements, the researchers found that most marine predators prefer Lévy-style locomotion when food is scarce. Even more interesting, the distribution of prey, such as krill, also fits the characteristics of Lévy flight.

Not only that, the foraging routes of amoeba, plankton, termites, bumblebees, large terrestrial herbivores, birds, and primates in the soil also follow similar patterns. Levy flight seems to be a common law for organisms to survive in an environment with scarce resources .

The Lévy flight pattern of a black-browed albatross. Image source: (DOI) 1 0.1073/pnas.1121201109

In fact, for wandering animals, finding the next meal depends not only on luck but also on advanced mathematics. In the case of knowing almost nothing about the distribution of prey, the efficiency of Levy flight is much higher than Brownian motion, which may be the reason why they switch to Levy flight mode when they try their luck.

Therefore, biologists later proposed the Lévy flight foraging hypothesis to summarize the animals' coquettish movements when they leave their fate to nature.

Not only wild animals, but many natural phenomena have the characteristics of Levi's flight.

For example, when water drips from a faucet, the time difference between the two drops of water is a Levy flight; the interval between two healthy heart beats, and even the trend of the stock market is a Levy flight.

When water drips from a faucet, the time difference between the two drops belongs to Levi's flight.

For example, the following graph shows the relationship between a stock price in Spain and the Spanish stock index:

After noticing the application space of Levy Flight in the notoriously unpredictable stock market, financial economists began to use Levy Flight to study financial markets .

Levy flights have even been used to study outbreaks of epidemics.

In 1997, programmer Hank Eskin wanted to know where all the money went, so he built a website.

By entering the serial number on the banknote and the local postal code into the above website, you can track the movement of the banknote. Some enthusiasts have even made a stamp of this website and put it on the banknote (red) to encourage people to use this website.

Users can enter their local postal code, banknote serial number and other information on the website to track the life history of the US dollar in their hands.

Eskin created this website just for fun, but later, Dirk Brockmann, a physicist at Humboldt University of Berlin, Germany, and his colleagues noticed this website when they were studying infectious diseases. They believed that the transmission route of infectious diseases was similar to that of banknotes, so they used the data from this website for analysis.

After analyzing the trajectories of 460,000 banknotes, they confirmed their conjecture: the spread of infectious diseases, like the spread of banknotes, conforms to the characteristics of Levy's flight. They published this research in the journal Nature in 2006.

Brockman's discovery was contrary to the mainstream epidemiological theory at the time (mainstream epidemiological theory holds that the probability of infection for everyone is the same), but Levy flights can predict the spread of diseases (such as SARS) better than traditional theories, so many epidemic models now use Levy flights .

Finally, don’t think that human behavior can escape the control of Levi’s flight. The trajectory of human beings when traveling and shopping also belongs to Levi’s flight. I didn’t expect that the shopping addicts and the flying flies are exactly the same.

Source: Bringing Science Home

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