🕳️ Black Hole Lensing Lab (2D)

This 2D companion drives the same Schwarzschild-metric physics as the 3D lensing lab through a plain top-down canvas built for reading the maths rather than orbiting a rendered disk: a side panel exposes the black hole's mass, a light ray's impact parameter, and a probe's orbit radius and velocity factor, while the canvas draws a fan of light rays whose bending is computed by integrating the real null-geodesic equation d²u/dφ² = −u+3Mu² (u=1/r) with 4th-order Runge–Kutta, alongside a test particle following the matching timelike geodesic that visibly precesses — or plunges through the innermost stable circular orbit — exactly as General Relativity predicts, with a live readout of the Schwarzschild radius, photon sphere, ISCO, critical impact parameter and deflection angle.