An elliptic curve over a finite field embedded on the characteristic zero curve with square symmetry.
The Hopf fibration S3→S2 pulls back curves on S2 to tori in S3. An elliptic curve E=C/Λ with square lattice Λ=Z+iZ maps to S2 via the Weierstrass ℘-function, and a curve on E traces out a curve on the corresponding Hopf torus after stereographic projection to R3.
This program renders the resulting space curve using three-gpu-pathtracer, producing a physically-based image with global illumination, reflections, and soft shadows.
Controls: Click and drag to orbit, scroll to zoom.
