  The synchronization of coupled oscillators is a fascinating manifestation of
self-organization that nature employs to orchestrate essential processes of
life, such as the beating of the heart. Although it was long thought that
synchrony or disorder were mutually exclusive steady states for a network of
identical oscillators, numerous theoretical studies in recent years have
revealed the intriguing possibility of `chimera states', in which the symmetry
of the oscillator population is broken into a synchronous and an asynchronous
part. However, a striking lack of empirical evidence raises the question of
whether chimeras are indeed characteristic to natural systems. This calls for a
palpable realization of chimera states without any fine-tuning, from which
physical mechanisms underlying their emergence can be uncovered. Here, we
devise a simple experiment with mechanical oscillators coupled in a
hierarchical network to show that chimeras emerge naturally from a competition
between two antagonistic synchronization patterns. We identify a wide spectrum
of complex states, encompassing and extending the set of previously described
chimeras. Our mathematical model shows that the self-organization observed in
our experiments is controlled by elementary dynamical equations from mechanics
that are ubiquitous in many natural and technological systems. The symmetry
breaking mechanism revealed by our experiments may thus be prevalent in systems
exhibiting collective behaviour, such as power grids, opto-mechanical crystals
or cells communicating via quorum sensing in microbial populations.
