  We give an algorithm that computes the final state of certain growth models
without computing all intermediate states. Our technique is based on a "least
action principle" which characterizes the odometer function of the growth
process. Starting from an approximation for the odometer, we successively
correct under- and overestimates and provably arrive at the correct final
state.
  Internal diffusion-limited aggregation (IDLA) is one of the models amenable
to our technique. The boundary fluctuations in IDLA were recently proved to be
at most logarithmic in the size of the growth cluster, but the constant in
front of the logarithm is still not known. As an application of our method, we
calculate the size of fluctuations over two orders of magnitude beyond previous
simulations, and use the results to estimate this constant.
