Ambient Intelligence (AmI) is an IT concept by which mobile users shall be seamlessly supported in their every-day activities. This includes interactions with remote resources as well as with their current physical environment. We have developed the so-called Ad hoc Service Grid (ASG) infrastructure that supports the latter form of interactions. It allows operators to cover arbitrary locations with Ambient Services in a Drop-and-Deploy fashion. An Ambient Service may autonomously distribute (replicate and migrate) within an ASG network to optimize its availability, response times, and network usage. In this paper, we propose a fully decentralized, dynamic, and adaptive service placement algorithm for AmI environments like the ASG. This algorithm achieves a coordinated global placement pattern that minimizes the communication costs without any central controller. It does not even require additional communication among the replicas. Moreover, placement patterns stabilize if no changes occur in the environment while replicas still retain their ability to adapt. Mechanisms for self-organized placement of services are very important for AmI environments in general since they allow for autonomous adaptations to dynamic changes and, thus, remove the need for manual (re)configuration of a running system. We present a detailed evaluation of the algorithm's performance and compare it with three other algorithms to show its competitiveness. Furthermore, we discuss how the desired self-organizing behavior emerges from the interactions of a few simple, local rules that govern the individual placement decisions. In order to do so, we give an in-depth analysis of a series of hidden effects that are not directly encoded into the placement algorithm but stem from its collective dynamics.