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It might start as a joke, a belief, or a rumor. At first, it's easy to dismiss. But then it gains a twist, builds momentum, and spreads like wildfire. What causes some ideas to die out while others take over the internet?

A new study in Â鶹ÒùÔºical Review Letters offers a fresh explanation. Led by researchers from the University of Vermont and the Santa Fe Institute, the work introduces a mathematical model for "self-reinforcing cascades," processes where the thing being spread, whether a belief, joke, or virus, evolves in real time and gains strength as it spreads.

Traditionally, scientists have used simple branching models to explain how things like ideas or diseases spread. One person gets infected or hears a rumor, they pass it to two more, each of those passes it to two more, and so on. It's a tree-like pattern in which the thing spreading (virus, belief, meme) stays the same. But this new research takes into account the fact that things don't just spread—they change as they spread, and that change actually helps them spread further.

"We were inspired in part by forest fires," says SFI Professor Sid Redner, a co-author on the paper. "Fires can grow stronger when burning through dense forest, and weaker when crossing open gaps. That same principle applies to information, jokes, or diseases. They can intensify or weaken depending on the conditions."

The model is simple in theory: each time an idea spreads, it has a chance of increasing or decreasing in intensity. If it weakens too much or finds no receptive audience, it dies out. But if it improves, even slightly, it can keep going, triggering large-scale cascades under a wide range of conditions.

This simple mechanism led to surprisingly complex results. Unlike classical models that require fine-tuned conditions to produce real-world-like patterns, the researchers' self-reinforcing cascade model naturally yielded "fat-tailed" distributions, statistical signatures often seen in viral social media posts and outbreaks. These include the observation that most posts or cases fizzle out quickly, but a few become massive, unpredictable hits.

"This kind of variability—where some things go viral while most don't—has often been explained by assuming the world is always near some critical tipping point," says lead author Laurent Hébert-Dufresne, a computer scientist at the University of Vermont and SFI External Professor. "But our model shows that if the quality of what's spreading can change as it spreads, you don't need to assume a special critical state. The variability just emerges naturally."

The implications extend far beyond theory. Juniper Lovato, study co-author and computer scientist at the University of Vermont, said the work could help researchers better understand belief formation, misinformation, and social contagion.

"This gives us a theoretical foundation for exploring how stories and narratives evolve and spread through networks," she says.

Next, the team plans to validate the model with real-world data from platforms like Bluesky, which allow researchers to distinguish between pure reposts and modified ones. The work may even circle back to its fiery origin.

"I'm excited to return to the forest fire model," Redner says. "What we've learned here gives us new tools to tackle that problem—and maybe others."