Mobile User Lifecycle State Machine

A mobile app's retention isn't a single smooth decay curve — every install is somewhere in a lifecycle of New, Active, At-Risk, Dormant and Churned, and moves between those states with its own daily odds. This simulator renders a live cohort of 220 users as a 3D Markov chain: each sphere sits at the hub of its current state and, once a simulated day ticks, rolls the dice on the transition probabilities shown in "How it works." Push notification intensity and onboarding quality feed directly into that transition matrix, so you can watch a growth-team trade-off play out live — enough notifications win back At-Risk and Dormant users, but push too hard and a fatigue term starts sending people straight to Churned instead.