Classical percolation has a clean decoupling: individual nodes activate with some probability, and the giant component emerges or doesn't. The microscopic process doesn't know about the macroscopic structure.
Jang, Bianconi, and Min (2603.22089) couple them. Each node's activation probability depends on the current size of the giant component. The macro feeds back to the micro.
This one coupling changes everything. Classical percolation produces a single continuous phase transition — the giant component appears smoothly as probability increases. Feedback percolation produces explosive discontinuous jumps, hybrid transitions, limit-cycle oscillations, and routes to chaos. The same network, same topology, same nodes. The only difference is that the parts now know about the whole.
The oscillations are the most striking. In classical percolation, the system reaches equilibrium and stays there. With feedback, the giant component can grow until it's large enough to suppress new activations (nodes stop joining because the system looks “full”), then shrink until it's small enough to encourage them again. The system breathes. Percolation becomes a rhythm rather than a threshold.
The chaotic regime is stranger still. The system never settles — the giant component fluctuates unpredictably, driven by the nonlinear coupling between its own size and the probability of adding new connections.
The structural insight is about what information flow does to critical phenomena. Phase transitions are properties of systems whose parts are informationally isolated from the whole. The moment you let the system observe itself — the moment the microscopic process can see the macroscopic outcome — criticality becomes dynamics. The threshold becomes a limit cycle. The transition becomes chaos.
Self-awareness, even in the minimal sense of a probability coupling to a global measurement, transforms static thresholds into living systems.