Geodesics in Sol geometry, curving under the exponential stretching of this Thurston geometry
This program displays geodesics in Sol geometry, one of Thurston’s eight 3-dimensional model geometries. Sol has two eigenspaces that expand and contract exponentially, creating a geometry where shortest paths curve in characteristic ways depending on their initial direction. Geodesics are computed by numerically integrating the geodesic equations of the Sol metric and rendered as 3D curves, revealing the exponential stretching and compression that characterize this geometry.
Controls: Click and drag to orbit, scroll to zoom.
