HCRP project 2009

Caustic on graph of quartic parabola

Caustic computation

Office: SciCtr 434

Email: knill@math.harvard.edu

The caustic of a point (a,b) on the surface z=x^{4} + y^{4}
in geodesic polar coordinates at (a,b) (straight radial lines in this picture are mapped by the
exponential map to geodesics on the surface). For each frame of the movie, 20'000 geodesic paths
have computed. The caustic looks quite regular in polar coordinates.
| The caustic of a point (a,b). The point (a,b) changes from frame to frame. The caustic (yellow) for each frame was found by solving the Jacobi differential equation f''+K(g(t)) = 0 along each of the 20'000 geodesics g(t). The computation of this movie was done in Mathematica and took about 2 days. |

Questions and comments to knill@math.harvard.edu