We are interested in the following problem: given the collection of critical values of a rational map (of the Riemann sphere), and the monodromy around these branch points, to recover the coefficients of the rational map (up to precomposition with a Mobius transformation).

One approach is to get an initial estimate via circle packing, and then to use Newton's method to adjust the coefficients. At the moment, this program implements simple circle packing (works OK for ~1000 circles; accurate, but not super fast). Rational map stuff to come.

The program can currently be used to produce pretty pictures like this one: