Where it shows up
The same inverse map appears anywhere a smooth field redirects what you sample. Refraction through a warm-air layer draws the shimmering mirage on a hot road by exactly this logic: sample the sky where the bent ray points, not where the object sits. Ray tracing a glass lens, tracing seismic waves through a slow patch of mantle, or reading a distorted reflection in a curved mirror all share the structure of one equation relating apparent position to true position through a deflection term. Astronomers even run it in reverse as a measuring tool, weighing dark matter by how much unseen mass is needed to produce the arcs we observe.
The knobs
- Lens mass (θ_E): sets the Einstein radius through . Heavier lenses bend light harder and grow the ring, swallowing more of the background into it.
- Source offset: biases where the source sits relative to the lens. At zero it sweeps straight through the centre for a full ring; push it out and the alignment stays lopsided, so you get lasting twin arcs instead.
- Background: swap the warped coordinate grid for a field of stars. In stars mode each background point is drawn at both of its image positions, brightening as it nears the ring.
- Einstein ring: overlays the faint circle of radius , the locus a perfectly aligned source collapses onto.