Why do some ideas spread like wildfire while others fade after a few conversations? From viral memes to political slogans, cascades of ideas ripple through societies in patterns that resemble, but never fully match, biological contagions. Researchers Laurent Hébert-Dufresne and Juniper Lovato of the University of Vermont are working to uncover the hidden mechanics of these dynamics. Their recent model, published in Physical Review Letters, treats ideas as “self-reinforcing cascades,” processes that can gain or lose strength as they spread.
The model draws inspiration from Canadian “zombie fires,” so intense they smolder underground through winter and reignite in spring. “We got really interested in that, because it is a complete change in the dynamics of forest fire,” Hébert-Dufresne said. “Just as fire can get more intense and survive what should extinguish it, beliefs can do the same. They get reinforced and, when strong enough, they spread through gaps where people might not be receptive.”
This analogy shaped the self-reinforcing cascade model. Unlike classical contagion models, where each infection or share is a faithful copy, this framework assumes that at every step an idea can improve with probability p or degrade with probability 1-p. In this view, stories are not static but mutate, sharpen, or distort as they pass from person to person.
The model relies on branching process mathematics, which represents a social network as a tree structure. In this structure, each person, or “node,” can transmit an idea to others, creating new “branches” as the idea spreads. In traditional models, large-scale spreading—known as “critical behavior”—only happens when conditions are exactly right, at a precise tipping point. In contrast, the new self-reinforcing cascade model adds the idea of reinforcement: as an idea spreads, it can get stronger or weaker each time it’s shared. For example, a story might become more convincing as people repeat it, or a product might improve as users modify it. This feedback effect generates critical-like behavior across a wide range of conditions, not just at a single balance point.
Researchers use recursive equations to track how cascade “intensity” grows or dies as it moves through the network. Calculations show that even below the critical threshold, cascades can display power-law size distributions. This means that while most ideas remain small, a few can reach massive scales. Such outcomes align more closely with what is observed in real social networks and online platforms, where a handful of ideas, videos, or rumors go viral while most fade quickly, something older models could not explain.
Applications of the model extend beyond theory. Public health campaigns depend on the spread of accurate information, while misinformation campaigns exploit the same dynamics. “Every time we create science, it can be used in two directions,” Lovato said. “There is always a cat-and-mouse game when you build new models to mitigate misinformation, because adversaries can also use them.”
The research also highlights how platform design influences the spread of ideas. “Platforms that allow only reposting constrain ideas to remain similar, while platforms with quote-posting or character limits create new mutation spaces,” Lovato said. In this way, platform architecture shapes the evolutionary landscape of stories.
Many open questions remain. “We still don’t know how things spread. We have many models and theories, but it is difficult to measure because ideas cannot be isolated the way microbes can,” Hébert-Dufresne said. Lovato pointed to the challenge of studying story mutations in real online data, and to the complexity of adaptive networks, where individuals alter connections based on what they encounter. The self-reinforcing cascade model offers a new perspective on the life of ideas. Rather than static messages, ideas emerge as dynamic cascades that evolve with each retelling. Like embers in a forest, they can reignite under the right conditions, reshaping the social landscape in ways researchers are only beginning to predict.