Information-theoretically secure schemes for sharing and modifying a secret among a dynamic swarm of computing devices are presented. The schemes securely and distributively maintain a global state for the swarm, and support an unlimited number of changes to the state according to (global) inputs received. We present proactively secure schemes supporting players joining and leaving the swarm. The schemes also allow swarms to be merged, cloned and split. We use the above schemes as a basis to implement an oblivious universal Turing machine, capable of evaluating dynamically specified functions.