🌀 3D Closed Timelike Curve — Temporal Loop

This simulation builds a genuine 3D spacetime diagram of a closed timelike curve (CTC): a circular worldline at coordinate radius r, in a rotating (Gödel-type) spacetime with rotation rate Ω. The critical radius r_c = arcsinh(1) / (Ω√2) marks the boundary where the local time-flow rate dτ/dt = 1 − (r/r_c)² turns negative. Below r_c the worldline climbs the time axis like an open helix; above it, the worldline closes on itself every circuit — a literal loop in 3D (x, z, t) space. A perturbation δ drives a self-consistency return map r_(n+1) = r_n + δ·sin(2πr_n/r_c), applied once per completed lap, so you can watch the loop's radius converge to a stable fixed point (self-consistent) or wander (unstable) as it repeats — a discrete stand-in for the boundary-value consistency problem Novikov's principle poses for CTCs. This replaces the original page's stub with a real Three.js worldline model, since the 2D original ("Temporal Time Loop Simulation") shipped only a placeholder canvas with no working mechanic.

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install