A qubit coupled to an environment evolves via the Lindblad equation: dρ/dt = −i[H,ρ] + γ(LρL† − ½{L†L,ρ}). Amplitude damping (decay |1⟩→|0⟩) shrinks the Bloch sphere toward the south pole. Dephasing destroys off-diagonal coherences, collapsing trajectories toward the z-axis. Watch the Bloch sphere trajectory in real time.