Viral Cascade Simulator

Social feeds don't spread information at a constant rate the way word-of-mouth does — they spread it through an algorithm that watches how much a post is already being engaged with and boosts its visibility accordingly, creating a reinforcing feedback loop distinct from simple contact-based contagion. This simulator tracks a single post moving through that loop round by round: some fraction of everyone who sees it engages, that engagement raises the algorithm's confidence in the post, the algorithm shows it to more people, and those people generate more engagement in turn. The whole loop reduces to a single reproduction-number-like threshold, R0 — above 1 the cascade compounds into a viral explosion, below 1 it fizzles out. Tune the base engagement rate and amplification factor, or switch algorithmic boost off entirely, to see exactly where that threshold sits.