Fast simulation of large-scale growth models

I'll describe a new algorithm to compute the final state of certain growth 
models without computing all intermediate states. The technique, which 
applies to both internal DLA and rotor-router aggregation, is based on a 
"least action principle" characterizing the odometer function of the 
growth process.  The algorithm takes as input an approximation of the 
odometer, and outputs the exact odometer.
Choosing the initial approximation to optimize the running time is an art 
form.

For a picture of a very large rotor-router aggregate (10^10 particles) 
computed by our algorithm, see

http://rotor-router.mpi-inf.mpg.de/10Bio/

Joint work with Tobias Friedrich.