We consider a cosmological scenario in which a scale-invariant spectrum of curvature perturbations is generated by a rapidly evolving equation of state on a slowly expanding background. This scenario generalizes the ‘‘adiabatic ekpyrotic’’ mechanism proposed recently by Khoury and Steinhardt [Phys. Rev. Lett. 104, 091301 (2010)]. Whereas the original proposal assumed a slowly contracting background, the present work shows that the mechanism works equally well on an expanding background. This greatly expands the realm of broader cosmological scenarios in which this mechanism can be embedded. We present a phase space analysis and show that both the expanding and contracting versions of the scenario are dynamical attractors, with the expanding branch having a broader basin of attraction. In both cases, a finite range of scale-invariant modes can be generated within the regime of validity of perturbation theory.