Taylor Rule 2D: Policy-Rate Phase Plane & Stability

Every modern central bank sets its policy rate roughly the way the Taylor Rule describes: a baseline real rate, plus extra tightening in proportion to how far inflation sits above target and how far output sits above trend. This 2D simulator renders that rule as a pannable, zoomable heat map over the inflation-gap / output-gap plane, drops a simulated economy onto it, and steps an IS-curve/Phillips-curve feedback loop quarter by quarter while a strip chart and a live eigenvalue dial track whether the trajectory is actually converging — computed exactly, not read off the textbook a_π>1 rule of thumb, which this simulation shows is an incomplete test once the output-gap weight and the underlying sensitivities are allowed to vary.