Alcubierre Warp Bubble: Spacetime Contraction & Expansion

This simulator renders the Alcubierre warp metric in 3D: a small ship sits inside a bubble of flat spacetime while a thin shell around it contracts space ahead and expands space behind, computed from the metric's own shape function f(r_s). A field of grid markers is advected by the metric's shift vector exactly as "Eulerian" observers would be dragged by the passing bubble, so the classic bunch-ahead / spread-behind warp pattern emerges from the real formula rather than a canned animation. Adjust the bubble's coordinate velocity, radius and wall thickness and watch the expansion scalar θ update live at the front and rear of the wall.