Is there any general rule that systems that have 'continuity' also having sensitivity to initial conditions? I can't help but think of chaos theory[0] when Freya describes the C2 continuous spline in the section on "Cascading Loss of Control" [1], and how it "yeets off to fucking wherever" (which is a great line).
Super good question. My thesis has both G2 and G4 continuous splines based on polynomial spirals ("spiro curves"), and the G4 definitely has more "wiggles," ie sensitivity to perturbations of the inputs. I imagine there is likely a general principle trading off locality with continuity, but am not able to quantify that rigorously.