A recently introduced model of macroevolution is studied on two different levels of systems analysis. Firstly, the systems dynamics and properties, above all the growth of complexity of the evolutionary units during the long-term evolution, are discussed, and, secondly, the complexity of the model itself, i.e. the richness of its various features, is studied with regard to a control parameter representing a background noise within the systems dynamics. The same is done with a randomized version of the model. The model is based on a normalized one-dimensional coupled map lattice with locally interacting sites representing different species. The evolution of the sites’ values representing the fitness of the species is governed by a usual diffusion rule and an additional memory- or random-based feedback loop. The introduction of a realistic background noise limiting the range of the feedback operation yields a pattern signature in fitness space with a distribution of temporal boost/mutation distances similar to a punctuated equilibrium behavior. Furthermore, the behavior of the mean lifetimes of “high” fitness values is correlated with the resolution-like parameter &Vegr; via a power law, a phenomenon called “fractal evolution.” Based on simple functional properties of the power law, an additional feedback loop is introduced to use the intrinsic fluctuations of the whole fitness landscape as a driving force to change adaptively the systems resolution. On long-term scales, the dynamical system properties exhibit a clear tendency towards progressive evolution potentials for each species. For both model versions, the memory-based and the random-based one, we achieve some basic mechanisms of evolutionary dynamics like coevolution, punctuated equilibrium with regard to internal or external changes during evolution, coordinated stasis for groups of species, and self-organized growth of complexity for all evolutionary units of the array leading to a kind of “Red-Queen-effect.” Additionally, for the memory based model a parameter was found indicating a limited range of noise allowing for the most complex behavior of the model, whereas the entropy of the system provides only a monotonous measure with respect to the varying noise level. ©1999 American Institute of Physics.