1. Critical Points of the Electric Field from a Collection of Point Charges

2. Computer Animation in Topology

Critical Points of the Electric Field from an Collection of Point Charges

The critical points in the electric field are useful in visualizing its geometrical and topological structure, and can help in understanding the forces and motion it induces on a charged ion or neutral dipole. Most visualization tools for vector fields use only samples of the field on the vertices of a regular grid, and some sort of interpolation, for example, trilinear, on the grid cells. There is less risk of missing or misinterpreting topological features if they can be derived directly from the analytic formula for the field, rather than from its samples. This work presents a method which is guaranteed to find all the critical points of the electric field from a finite set of point charges. To visualize the field topology, we have modified the saddle connector method to use the analytic formula for the field.

Computer Animation in Topology

Two short computer animated films visualizing fractal curves and surfaces will be shown – ’Zooms on Self Similar Figures’, and ’Homage to Hilbert’ – and the longer film ’Turning a Sphere Inside Out’, about a regular homotopy which does that without tearing or creasing the sphere, by passing the surface through itself. The production of these films, two of which were completed 30 years ago, will be discussed.