The significance of our analyses is in showing that attractor dynamics may push a system towards reproduction. Further, our data predicts pronounced enhancement of the probability for spontaneous emergence of a self-reproducing chemical entity out of a randomly disposed chaotic environment. This is observed in the dynamic transition towards the same attractor from a variety of initial assembly compositions. The presence of unique self-reproducing dynamic attractors was verified for a multitude of different parameterized environments, reflecting the generality of this finding to systems in which molecular assemblies accrete spontaneously. We also show that for multi-attractor systems, specific environmental changes lead to a transition from one attractor to another. This characteristic is considered a predictor for evolutionary capacity , transiting from one reproducing attractor to another.