HCRP project 2009
Caustic on graph of quartic parabola
Caustic of parabola
Office: SciCtr 434

Click to see larger
Geodesics on the paraboloid. This was a test picture after replacing the canned DSolve routines with own Runge Kutta routines which is necessary when doing the evolution on manifolds with different charts and also allows a bit more control in general like assuring that the flow stays on the unit tangent bundle. The surface is the elliptic paraboloid z=x2 + 2 y2.

Click to see larger
Same picture but with wave fronts added.

Click to see larger
Geodesics and wave fronts on the monkey saddle surface z = 6 x y2-2x3-3y4.
Questions and comments to knill@math.harvard.edu
Oliver Knill | Department of Mathematics | Harvard University