Black Hole Lensing

General relativistic gravitational ray-tracing showing the extreme light bending, photon sphere ring, and Doppler-beamed accretion disk.

Playground

60 FPS • Canvas 2D

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Live Parameters

Schwarzschild Radius (rs) 36

Event horizon radius

Mathematical Formulation

79 chars high

Analytical Equation

\hat{\alpha} = \frac{4GM}{c^2 b} = \frac{2 r_s}{b}, \quad r_s = \frac{2GM}{c^2}, \quad I_{\text{obs}} = I_{\text{emit}} \cdot \delta^4

Compact Formula

v_orb = 2.5 / √r, y_warp = y - (1.5*rs / d)*22, doppler_hue = 190 + 30*sin(θ)

Renderer Logic

if (d > rs && rawY < 0) {
  const bend = (rs * 1.5) / d;
  warpedY = rawY - bend * 22;
}
const doppler = Math.sin(ang[i]);
const hue = doppler > 0 ? 190 + doppler * 30 : 25 + Math.abs(doppler) * 20;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#black-hole #general-relativity #lensing #astrophysics #space #gravity

Author: Math Art Core Target: 60 FPS

Black Hole Lensing

Live Parameters

Mathematical Formulation

Mathematical Tags

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