Square-lattice elliptic curve embedded in R4 via the Weierstrass functions.
The Weierstrass ℘-function for the square lattice Λ=Z+iZ uniformizes an elliptic curve with Z/4 automorphism symmetry. The map ℘:C/Λ→CP1≅S2 combined with the Hopf fibration S3→S2 lifts features of the elliptic curve to surfaces and curves in S3, stereographically projected to R3 for visualization.
The geometry is rendered using three-gpu-pathtracer for physically-based global illumination with soft shadows and interreflections, revealing the four-fold symmetry inherited from the square lattice.
Controls: Click and drag to orbit, scroll to zoom.
