Alcubierre Warp Bubble 2D Cross-Section: Spacetime Contraction & Expansion

This simulator renders the exact z=0 plane of the Alcubierre warp metric: 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 grid of spacetime 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. A live profile graph plots f(r) and the expansion scalar θ(r) against radial distance as you adjust the bubble's coordinate velocity, radius and wall thickness — drag the main view to pan and scroll to zoom.