A camera-screen feedback loop is a physical system that iterates a differential equation

Jack cites Jim Crutchfield’s 1984 ‘Space-Time Dynamics in Video Feedback’: a camera pointing at a monitor is a physical system that can perform computation equivalent to iterating a differential equation. A differential equation describes a state that updates as a function of its own current state, which is exactly what a feedback frame does, each frame a tiny modification of the one before. This reframes visual feedback as a meaningful simulation model, not just an aesthetic trick, and connects to fluid-dynamics and reaction-diffusion systems, whose complex behaviour also emerges from simple local update rules applied repeatedly.

Examples

Jack notes the same feedback structure underlies fluid-simulation equations that update ‘pressure and velocity at each point’ continuously, and that GPUs only recently made such highly parallel operations easy to run in real time.

Assessment

State the connection Crutchfield draws between video feedback and differential equations. Name one physical phenomenon such a loop can model, and say why the feedback structure enables that modelling.