Francesco De Comité
Associate Professor of COmputer Science
University of Sciences, Lille, France
Manipulation of digital images, and use of ray-tracing software can help you to concretize mathematical concepts. Either for giving you an idea of how a real object will look (as with my work on playing cards slide-together presented at Bridges 2010), or to represent imaginary landscapes only computers can handle.
Designing Doyle spirals, then transforming them with Mobius transforms which preserve the circles' tangency, is an endlessly rewarding process. One always find some nuggets.
The basic circle packing template is obtained by recursively filling Apollonian Gaskets. Transforming each circle into a cylinder, then controlling its height, generates fascinating three dimensionnal objects.