A Circle Packing Algorithm

. A circle packing is a configuration P of circles realizing a specified pattern of tangencies. We describe an efficient algorithm for computing the radii of packings in euclidean and hyperbolic geometry, discuss its performance, and illustrate some recent applications. Introduction A circle packing is a configuration P of circles realizing a specified pattern of tangencies. As such, it enjoys dual natures --- combinatoric in the pattern of tangencies, encoded in an abstract "complex" K, and geometric in the radii of the circles, represented by a radius "label" R. As an early example, Figure 1 displays a simple complex K and a circle packing having its combinatorics. More substantial packings may involve over 100,000 circles. Figure 1. A simple packing example Key words and phrases. circle packing, conformal geometry, discrete Dirichlet problem. The second author gratefully acknowledges support of the National Science Foundation and the Tennessee Science Alliance. 2 CHARLES R. COL..