How Black Hole Ray Tracing Works
The core idea: trace rays backwards
If you want to render an image, you can imagine a camera with pixels. Each pixel corresponds to a direction in the camera’s sky. In ordinary graphics, you can cast a ray forward into a scene.
In curved spacetime, you can still do something similar: for each pixel direction, integrate the path of a light ray (a null geodesic). Many renderers do this backwards: start at the camera and follow the ray outwards to see what it hits (or which direction on a background sky it samples).
What equation is being solved?
The “ray” is not a straight line in Euclidean space; it’s a curve determined by the spacetime metric. At a conceptual level, the ray tracing step is: choose initial position + initial direction at the camera, then integrate the geodesic equations.
If you want the math-heavy version, your site already has it: Ray tracing in the Schwarzschild geometry and the backwards ray tracing algorithm.
Impact parameter (why one number matters a lot)
For spherically symmetric black holes, many qualitative features depend on how “close” the light ray comes to the black hole. A common way to summarize that is an impact parameter, which you can think of (loosely) as “how much sideways offset the ray has” relative to the hole.
Rays with some impact parameters get deflected and escape; others get captured. Near the boundary between those outcomes, small changes can create huge visual differences.
Why do you get rings and repeated structure?
Some rays skim near the unstable photon orbits (photon sphere). Those rays can loop around the black hole one or more times before escaping. Each extra loop tends to map the background sky again, producing thinner “higher order” rings.
That’s why black hole visuals often show nested structure—even if the original background image is simple.
What this site’s simulator computes (high level)
Your Black Hole Image Simulation takes an uploaded image and uses a lensing model to remap pixels based on how light would be bent. The important thing for users: the output is an educational visualization of gravitational lensing, not a claim about a specific real telescope observation.
If you want a more geometry-first view (instead of an image warp), the embedding diagram pages provide another intuition: black hole embedded diagram.