We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium configuration. Specifically we observe a transition from an in phase correlated motion via phase randomized oscillations towards oscillations with a phase difference π between adjacent particles thereby yielding the growth of long time transient spatiotemporal oscillation patterns. Parameter modifications allow for designing these patterns, including steady states and even states that combine in phase and correlated out of phase oscillations along the chain. The complex relaxation dynamics is based on finite size effects together with an evolution running from the nonlinear to the linear regime thereby providing a highly unbalanced population of the center of mass and relative motion.Introduction Nonlinear dynamics is at the heart of the emergence of structure and complexity in nonequilibrium systems ranging from pattern formation in biological [1-3], chemical [1,4,5] and physical systems [3,6] via the emergence of solitons, kinks and breathers in coupled nonlinear oscillators [7] to the synchronization of self-sustained [8-10] and chaotic oscillators [10,11]. In view of the formidable progress achieved in recent years with respect to the cooling and trapping of particles [12,13] and the control of their interactions [14], it is highly desirable to study the emergence of structure and complexity out of equilibrium with the extremely well controlled and prepared ensembles provided by cold atoms in optical lattices [13,15] and ions in microtraps [16,17]. Specifically for ions it is known that they possess already for their equilibrium a plethora of different configurations, such as zig-zag chains [18,19] and ion crystals possessing concentric rings (2D), shells (3D) [20] and 'string-of-disks' configurations [21]. Even two component Coulomb bicrystals exhibiting cylindrical structures coexisting with structures of spheroidal shape could be observed [22]. Recent examples following the route of structure formation out of equilibrium include the pattern formation of trapped ions in an array of optical microtraps [23], the growth of density waves in driven superlattices [24] and the emergence of dynamical current reversals associated with peaked velocity distributions for dilute long range interacting particles in driven lattices [25]. Here, we explore the complex pathway a highly excited, nonlinear chain of interacting particles takes in a dissipative periodic potential towards its asymptotic equilibrium configuration. We hereby demonstrate the emergence of a transition from initially in phase correlated motion via phase randomized oscillations towards oscillations with a