TORONTO -- A new study from George Washington University suggests that early online support for the extremist group the Boogaloos, also known as the Boogaloo Boys or "Bois", followed a similar mathematical pattern as that of the Islamic State, despite the stark differences in ideology, location and culture.

The Boogaloos, one of the groups who took part in the Jan. 2021 attack on the U.S. Capitol, is a loosely affiliated pro-gun rights movement that wants a second civil war in America, and often aligns itself with far-right and white nationalist movements.

The study,, compared the growth of the Boogaloo movement, which is mostly based in the U.S., to online support for ISIS, the terrorist group mostly based in the Middle East.

The study stresses that the goal of the research is not to provide “a philosophical, psychological, economic or sociopolitical analysis of such movements,” but instead to find an explanation of their online growth by “comparing a mathematical model of aggregation to empirical data.”

“Despite their differences, extremist movements may share common system-level dynamics,” the study posits, adding that researchers are “focusing on possible shared mechanics of their online growth processes, with the purpose of identifying any common mechanical patterns that might arise and seeking a better understanding of how online violent movements emerge and grow.”

Researchers collected data from public social media platforms like Facebook and VKontakte, searching for posts from supportive groups using hashtags and keywords for both the Boogaloos and ISIS, and mapping a network of content that ranged from fundraising to real-time operational information.

After analyzing the online support for both groups, the study found that the evolution of both movements follows a “single shockwave mathematical equation.”

Researchers compared their shockwave equation, into which they inputted values for things like aggregation probability and pool size for potential online recruits, to a single equation in physics explaining the different trajectories of different objects.

"This study helps provide a better understanding of the emergence of extremist movements in the U.S. and worldwide," said study author Neil Johnson . "By identifying hidden common patterns in what seem to be completely unrelated movements, topped with a rigorous mathematical description of how they develop, our findings could help social media platforms disrupt the growth of such extremist groups."

Specifically, the study says the mathematical theory suggests that social media platforms can mitigate the growth of new forms of online extremism by nudging the “collective chemistry” of online movements.

"One key aspect we identified is how these extremist groups assemble and combine into communities, a quality we call their 'collective chemistry'," said study co-author Yonatan Lupu in the release. “Despite the sociological and ideological differences in these groups, they share a similar collective chemistry in terms of how communities grow. This knowledge is key to identifying how to slow them down or even prevent them from forming in the first place."

The study suggests the need for specific policies aimed at limiting the growth and support of extremist movements.

Social media platforms have struggled to control the growth of online extremism, the study says, as they often use a combination of content moderation and active promotion of users who are providing counter messaging.

The researchers point out the limitations in both approaches and suggest that new strategies are needed to combat online extremism, such as altering algorithms which suggest content to social media users – but may also be nudging potential recruits towards extremist groups.

“Platforms already use algorithms to provide users with recommendations of groups to join, including extremist groups to the extent platforms’ algorithms predict users would be interested in such groups,” the study says.

Researcher’s caution that online movements can show “remarkably quick growth and adaptation,” and that current strategies – including content moderation and sometimes total deplatforming of groups – has the disadvantage of being “highly visible” and can sometimes “provoke and energize extremists.”

The study also says that efforts to stem online extremism can be avoided by extremists when they simply move their support and members to unmoderated platforms, and therefore social media platforms should focus on “flattening the curve” of movements by disrupting their “collective chemistry” or their assembly into communities.