Both systems share the same fixed point. The same equation is satisfied. But the dynamics that hold them there could not be more different.
The passive fixed point is a destination. A marble rolls to the bottom of a bowl. Friction dissipates energy. Motion ceases. The equation is solved by the elimination of time — once the particle arrives, nothing further happens. Convergence is a kind of death.
The active fixed point is a process. The system never sits exactly at x*. It orbits, jitters, overshoots and corrects. Each displacement generates an error; each error drives a response. The equation is solved not once but continuously, re-derived at every moment by a mechanism that refuses to stop computing.
A spiking neuron that solves an equation. A cell that maintains its temperature. A mind that reconstructs itself each morning. These are not converging — they are correcting.
Life is an active fixed point.