Abstract. Dynamical structure in the brain promotes biological function. Natural scientists look for correlations between measured electrical signals and behavior or mental states. Computational scientists have new opportunities to receive ’algorithmic’ inspiration from brain processes and propose computational paradigms. Thus a tradition which dates back to the 1940s with neural nets research is renewed. Real processes in the brain are ’complex’ and withstand trivial descriptions. However, dynamical complexity need not be at odds with a computational description of the phenomena and with the inspiration for algorithms that actually compute something in an engineering sense. We engage this complexity from a computational viewpoint, not excluding dynamical regimes that a number of authors are willing to label as chaos. The key question is: what may we be missing computation-wise if we overlook brain dynamics? At this point in brain research, we are happy if we can at least provi...