Menus Subscribe Search

Follow us


levy-model

An example of 1,000 steps of an approximation of Lévy flight in two dimensions. (ILLUSTRATION: PUBLIC DOMAIN)

Mapping (and Potentially Preventing) Crime With Math

• September 17, 2013 • 10:00 AM

An example of 1,000 steps of an approximation of Lévy flight in two dimensions. (ILLUSTRATION: PUBLIC DOMAIN)

Mathematicians propose using the “Lévy flight” model to reveal and police hotspots of crime.

Mathematicians have long tried to bring order to chaos—to develop complex models to understand seemingly random events. One particularly versatile model has been the “Lévy flight,” a pattern of movement that consists of short, frequent steps all clustered in one area, and is then punctuated by long walks to a separate area. Picture wild animals foraging for food in a field, or searching an ocean for prey: they’ll slowly use up all the resources in one small area, and then move to a new area and start eating or hunting again there.

The Lévy flight, named after French mathematician Paul Lévy, has been used to describe phenomena as wide-ranging as financial markets, earthquakes, and a child’s game of hide-and-seek. In recent years, it has even been used to analyze patterns as dreary as the Web-surfing habits of online consumers, and as fascinating as the drips and streaks of Jackson Pollock’s paintings.

But now, a group of mathematicians argue that the Lévy pattern may have an even more practical, real-world application: mapping—and potentially preventing—crime.

“If the relationship between a burglar’s movement and choice of targets becomes better elucidated, then the police will be better informed when they schedule their nightly patrols.”

A group of math students and professors, writing in a recent issue of SIAM Journal on Applied Mathematics, expand on the previous hypothesis that a human’s daily and weekly commute can often resemble an animal’s foraging path. (For instance, a person may take short walks around her neighborhood on the weekend, and then take a relatively long bus or subway ride to work during the week, followed by short walks in the vicinity of the office.)

The authors of this new article build on that idea, and hypothesize that crime might work the same way. For instance, a burglar might try to break into a group of homes in one localized area over the course of several days, and then, after a while, might travel to a new neighborhood for another cluster of break-ins. Short steps, long leap, short steps: the Lévy flight model.

In this article, authors Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov, and Scott McCalla, compared burglary data to the step sizes and lengths in a typical Levy flight pattern.

“There is actually a relationship between how far these criminals are willing to travel for a target and the ability for a hotspot to form,” said Kolokolnikov and McCalla. They argued that while law enforcement agencies normally record information about the location and times of discrete crimes in an area, they don’t yet have a widely-accepted method for tracking—let alone predicting—the movement of individual criminals. “In our research, we have seen a relationship between the dynamics of burglary hotspots and the way criminals move.”

So what could this all mean for crime prevention, on the local level, in the real world? The authors say that law enforcement agencies need to think bigger.

“Certain policing efforts concentrate on known offenders’ home territories as a predictor of future crimes,” Kolokolnikov and McCalla said. “If the relationship between a burglar’s movement and choice of targets becomes better elucidated, then the police will be better informed when they schedule their nightly patrols.”

The authors do seem aware of how vague this all may sound. It may be a bit far-fetched to imagine the New York Police Department, for example, employing a fractal geometrist to help it stop the next break-in from happening.

“Applying models like ours to reproduce the data is a strong first step, but there is clearly more work to be done,” said Kolokolnikov and McCalla. “This would have clear implications for policing policy, and could have a significant impact on burglary rates.”

Still, further research in this area could yield another small tool in the big belt of law enforcement. And it’s (arguably) a better use of our mathematicians’ valuable time than mapping a Pollock painting.

Lauren Kirchner
Lauren Kirchner is the Web editor of The Baffler. She has written for the Columbia Journalism Review, Capital New York, Slate, The Awl, The Hairpin, and many others. Follow her on Twitter @lkirchner.

More From Lauren Kirchner

A weekly roundup of the best of Pacific Standard and PSmag.com, delivered straight to your inbox.

Recent Posts

October 30 • 5:08 AM

We’re Not So Great at Rejecting Each Other

And it’s probably something we should work on.


October 30 • 4:00 AM

He’s Definitely a Liberal—Just Check Out His Brain Scan

New research finds political ideology can be easily determined by examining how one’s brain reacts to disgusting images.


October 29 • 4:00 PM

Should We Prosecute Climate Change Protesters Who Break the Law?

A conversation with Bristol County, Massachusetts, District Attorney Sam Sutter, who dropped steep charges against two climate change protesters.


October 29 • 2:23 PM

Innovation Geography: The Beginning of the End for Silicon Valley

Will a lack of affordable housing hinder the growth of creative start-ups?


October 29 • 2:00 PM

Trapped in the Tobacco Debt Trap

A refinance of Niagara County, New York’s tobacco bonds was good news—but for investors, not taxpayers.


October 29 • 12:00 PM

Purity and Self-Mutilation in Thailand

During the nine-day Phuket Vegetarian Festival, a group of chosen ones known as the mah song torture themselves in order to redirect bad luck and misfortune away from their communities and ensure a year of prosperity.


October 29 • 10:00 AM

Can Proposition 47 Solve California’s Problem With Mass Incarceration?

Reducing penalties for low-level felonies could be the next step in rolling back draconian sentencing laws and addressing the criminal justice system’s long legacy of racism.


October 29 • 9:00 AM

Chronic Fatigue Syndrome and the Brain

Neuroscientists find less—but potentially stronger—white matter in the brains of patients with CFS.


October 29 • 8:00 AM

America’s Bathrooms Are a Total Failure

No matter which American bathroom is crowned in this year’s America’s Best Restroom contest, it will still have a host of terrible flaws.



October 29 • 6:00 AM

Tell Us What You Really Think

In politics, are we always just looking out for No. 1?


October 29 • 4:00 AM

Racial Resentment Drives Tea Party Membership

New research finds a strong link between tea party membership and anti-black feelings.


October 28 • 4:00 PM

The New Health App on Apple’s iOS 8 Is Literally Dangerous

Design isn’t neutral. Design is a picture of inequality, of systems of power, and domination both subtle and not. Apple should know that.


October 28 • 2:00 PM

And You Thought Your Credit Card Debt Was Bad

In Niagara County, New York, leaders took on 40-year debt to pay for short-term stuff, a case study in the perverse incentives tobacco bonds create.



October 28 • 10:00 AM

How Valuable Is It to Cure a Disease?

It depends on the disease—for some, breast cancer and AIDS for example, non-curative therapy that can extend life a little or a lot is considered invaluable. For hepatitis C, it seems that society and the insurance industry have decided that curative therapy simply costs too much.


October 28 • 8:00 AM

Can We Read Our Way Out of Sadness?

How books can help save lives.



October 28 • 6:15 AM

Incumbents, Pray for Rain

Come next Tuesday, rain could push voters toward safer, more predictable candidates.


October 28 • 6:00 AM

Why Women Are Such a Minority in Elected Office

The obvious answers aren’t necessarily the most accurate. Here, five studies help clear up the gender disparity in politics.


October 28 • 4:00 AM

The Study of Science Leads to Leftward Leanings

Researchers report the scientific ethos tends to produce a mindset that favors liberal political positions.


October 28 • 2:00 AM

Who Funded That? The Names and Numbers Behind the Research in Our Latest Issue

This list includes studies cited in our pages that received funding from a source other than the researchers’ home institutions. Only principal or corresponding authors are listed.


October 27 • 4:00 PM

School Shootings: What’s Different About Europe?

There may be a lot of issues at play, but it’s undeniable that the ease of access to guns in the United States is a major contributing factor to our ongoing school shooting crisis.


October 27 • 2:00 PM

The Best Investigative Reporting on Campaign Finance Since 2012

From dark money to a mysterious super PAC donor, here are a few of the best investigations of money in politics since the last elections.


October 27 • 12:00 PM

Could Economics Benefit From Computer Science Thinking?

Computational complexity could offer new insight into old ideas in biology and, yes, even the dismal science.


Follow us


We’re Not So Great at Rejecting Each Other

And it's probably something we should work on.

Chronic Fatigue Syndrome and the Brain

Neuroscientists find less—but potentially stronger—white matter in the brains of patients with CFS.

Incumbents, Pray for Rain

Come next Tuesday, rain could push voters toward safer, more predictable candidates.

Could Economics Benefit From Computer Science Thinking?

Computational complexity could offer new insight into old ideas in biology and, yes, even the dismal science.

Politicians Really Aren’t Better Decision Makers

Politicians took part in a classic choice experiment but failed to do better than the rest of us.

The Big One

One town, Champlain, New York, was the source of nearly half the scams targeting small businesses in the United States last year. November/December 2014

Copyright © 2014 by Pacific Standard and The Miller-McCune Center for Research, Media, and Public Policy. All Rights Reserved.