A rotating black hole, drawn by solving Einstein's equations for the path of every ray of light — one per pixel, sixty times a second.
Nothing here is a texture, a model, or an animation. Every frame, for every pixel on your screen, this page fires a ray of light backwards from your eye and integrates its path through curved spacetime until it either escapes to the stars or falls through the event horizon.
The black hole is described by the Kerr metric — the exact solution of Einstein's field equations for a rotating mass, found by Roy Kerr in 1963. Light paths are computed by integrating the null geodesic equations in Boyer–Lindquist coordinates using a Hamiltonian formulation and a fourth-order Runge–Kutta integrator with adaptive step size. Set spin to zero and the equations collapse exactly to Schwarzschild's 1916 solution, the first ever found.
That band arcing above and below the shadow is not a halo. It is the far side of the disk, behind the black hole, whose light is bent up over the top and under the bottom and delivered to your eye. You are seeing around an object. Gravity is acting as a lens.
The disk orbits at a large fraction of the speed of light. The side rotating toward you has its light beamed forward and blueshifted; the side rotating away is dimmed and reddened. This is relativistic Doppler beaming, and the brightness ratio across the disk is computed properly, as g⁴, where g is the full frequency shift including gravitational redshift climbing out of the well.
The sharp circle hugging the shadow is the photon sphere — the radius where gravity is strong enough that light orbits the hole. Stars smeared around that ring are objects sitting directly behind the black hole, their light wrapped a full half-turn around it. That is an Einstein ring, and it is why we can weigh galaxies we cannot see.
Your clock ticks in your own proper time. The Earth clock ticks in the coordinate time of an observer infinitely far away. As you fall inward they diverge — not as a graphic, but as the ratio √(ΣΔ/A) falling out of the metric at your position. At the horizon it goes to infinity: from outside, you would appear to slow, redden, and freeze there forever.
Exactly two liberties. The accretion disk is drawn at a few thousand kelvin so it glows visible orange — a real one around a stellar-mass hole radiates in X-rays and would be invisible to your eye. And the disk is geometrically thin, with brightness textured by procedural noise rather than a magnetohydrodynamic simulation. Everything about how the light travels is honest.
Written by Claude Opus 5 for Stephen Longo. One HTML file, no libraries, no assets, no network calls. The renderer is roughly three hundred lines of GLSL.