Welcome to the lab.

Shaders & WebGL ·
Gravity as a raw material

Drag to tilt · arrow keys work too

[ How it's built ]

No meshes, no assets: the entire image is one fragment shader. Every pixel integrates a real null geodesic. Instead of stepping along a distance and nudging the direction with a 1/r² pull, it solves the Schwarzschild orbit equation for u = 1/r and marches in the angle swept around the hole, which costs about the same and is actually right.

// d²u/dφ² = -u + 3M u², velocity verlet, 112 steps of 0.085 rad
u   += du * DPHI + 0.5 * acc * DPHI * DPHI;
acc  = -u + 3.0 * MASS * u * u;

That one change buys the things the approximation can't: a shadow of exactly 3√3 M across, an unstable photon sphere at 3M, and rays that wind far enough around the hole to fold the disk into second and third images. The thin ring at the edge of the shadow is not drawn: it is those images stacking up. Drag (or scroll, or use the arrow keys) to tilt: at edge-on, the far side of the disk is lensed up over the top and closed under the bottom into a full halo.

The disk is a slab of turbulent fBm rotating Kepler-style, inner material faster. It emits and it absorbs, so its near rim occludes its far one. Each crossing carries the relativistic frequency shift (orbital doppler against the photon's own direction, times the gravitational redshift), and that shift is applied as colour and as beaming, not just brightness. The approaching side runs blue and burns; the receding side falls to a dim red.

// how much bluer and brighter: observed / emitted frequency
float shift = grav / (gamma * (1.0 - beta * mu));
float emis  = dens * pow(shift, 1.35);
emis /= 1.0 + emis * 0.30;  // ceiling: clipping erases colour

Everything else is sampling. The stars sit on an equal-angle grid and each one is drawn at least as wide as the pixel it lands on, so none of them can fall between samples and scintillate; where a ray has wound far enough that the lens is squeezing a whole patch of sky into a hairline, they widen and dim rather than pretending to be points. The march writes linear HDR light into a half-float buffer; a half-resolution bloom lifts the ring and the disk's inner edge, then one grade pass tone-maps, adds film grain sized to the device pixel, dithers, and vignettes.