  Spatio-temporally extended nonlinear systems often exhibit a remarkable
complexity in space and time. In many cases, extensive datasets of such systems
are difficult to obtain, yet needed for a range of applications. Here, we
present a method to generate synthetic time series or fields that reproduce
statistical multi-scale features of complex systems. The method is based on a
hierarchical refinement employing transition probability density functions
(PDFs) from one scale to another. We address the case in which such PDFs can be
obtained from experimental measurements or simulations and then used to
generate arbitrarily large synthetic datasets. The validity of our approach is
demonstrated at the example of an experimental dataset of high Reynolds number
turbulence.
