Simulating a shared register can mask the intricacies of designing algorithms for asynchronous message-passing systems subject to crash failures, since it allows them to run algorithms designed for the simpler shared-memory model. The simulation replicates the value of the register in multiple servers and requires readers and writers to communicate with a majority of servers. The success of this approach for static systems, where the set of nodes (readers, writers, and servers) is fixed, has motivated several similar simulations for dynamic systems , where nodes may enter and leave. However, all existing simulations need to assume that the system eventually stops changing for a long enough period or that the system size is fixed. This paper presents the first simulation of an atomic read/write register in a crash-prone asynchronous system that can change size and withstand nodes continually entering and leaving. The simulation allows the system to keep changing, provided that the number of nodes entering and leaving during a fixed time interval is at most a constant fraction of the current system size.