Menus Subscribe Search
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

August 1 • 4:00 PM

The Gaps in Federal Law That Are Making It Easy for Lenders to Sue Soldiers

Courts are required to appoint attorneys for service members if they are sued and can’t appear. But the law says little about what those lawyers must do. Some companies have taken advantage.


August 1 • 2:22 PM

Warmer Parenting Makes Antisocial Toddlers More Empathetic

Loving care may be the best antidote to callous behavior in young children.


August 1 • 2:00 PM

The Federal Health Insurance Exchange Remains Surprisingly Active

New federal data, obtained by ProPublica under the Freedom of Information Act, shows nearly one million insurance transactions since mid-April.



August 1 • 6:00 AM

The Idea of Racial Hierarchy Remains Entrenched in Americans’ Psyches

New research finds white faces are most closely associated with positive thoughts and feelings.


August 1 • 4:00 AM

How and Why Does the Social Become Biological?

To get closer to an answer, it’s helpful to look at two things we’ve taught ourselves over time: reading and math.



July 31 • 4:00 PM

Thank You for Your Service: How One Company Sues Soldiers Worldwide

With stores near military bases across the country, the retailer USA Discounters offers easy credit to service members. But when those loans go bad, the company uses the local courts near its Virginia headquarters to file suits by the thousands.


July 31 • 2:00 PM

A New York State of Fracking

Court cases. A governor’s moratorium. Pending health study. A quick guide to the state of fracking in New York.


July 31 • 11:17 AM

How California Could Power Itself Using Nothing but Renewables

We don’t need fossil fuels.


July 31 • 8:00 AM

Should Athletes Train Their Memories?

Sure, but it probably won’t help.


July 31 • 6:00 AM

Universal Basic Income: Something We Can All Agree on?

According to Almaz Zelleke, it’s not a crazy thought.


July 31 • 4:00 AM

Medical Dramas Produce Misinformed, Fatalistic Viewers

New research suggests TV doctor dramas leave viewers with skewed impressions of important health-related topics.


July 30 • 4:00 PM

Still the World’s Top Military Spender

Although declining in real terms, the United States’ military budget remains substantial and a huge drain on our public resources.



July 30 • 2:04 PM

The Rise of the Nuisance Flood

Minor floods are afflicting parts of Maryland nearly 10 times more often than was the case in the 1960s.


July 30 • 2:00 PM

The (Mostly Awful) Things You Learn After Investigating Unpaid Internships for a Year

Though the intern economy remains opaque, dialogue about the role of interns in the labor force—and protections they deserve—is beginning to take shape.


July 30 • 12:00 PM

Why Coffee Shortages Won’t Change the Price of Your Frappuccino

You’re so loyal to Starbucks—and the company knows it—that your daily serving of caffeine is already marked up beyond the reach of any fluctuations in supply.



July 30 • 10:00 AM

Having Difficult Conversations With Your Children

Why it’s necessary, and how to do it.


July 30 • 8:00 AM

How to Make a Convincing Sci-Fi Movie on a Tight Budget

Coherence is a good movie, and its initial shoot cost about the same amount of money as a used Prius.


July 30 • 6:00 AM

Are You Really as Happy as You Say You Are?

Researchers find a universal positivity bias in the way we talk, tweet, and write.


July 30 • 4:00 AM

The Declining Wage Gap for Gay Men

New research finds gay men in America are rapidly catching up with straight married men in terms of wages.


July 30 • 2:00 AM

LeBron James Migration: Big Chef Seeking Small Pond

The King’s return to Cleveland is a symbol for the dramatic shift in domestic as well as international migration.


July 29 • 4:00 PM

Are Children Seeking Refuge Turning More Americans Against Undocumented Immigrants?

A look at Pew Research Center survey data collected in February and July of this year.


Follow us


Subscribe Now

Warmer Parenting Makes Antisocial Toddlers More Empathetic

Loving care may be the best antidote to callous behavior in young children.

The Rise of the Nuisance Flood

Minor floods are afflicting parts of Maryland nearly 10 times more often than was the case in the 1960s.

America’s Streams Are Awash With Pesticides Banned in Europe

You may have never heard of clothianidin, but it's probably in your local river.

How Textbooks Have Changed the Face of War

War is more personal, less glorious, and more hellish in modern textbooks than in the past. But there’s still room for improvement.

The Big One

One in two full-time American fast-food workers' families are enrolled in public assistance programs, at a cost of $7 billion per year. July/August 2014

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