The observation of ideal four-wave mixing dynamics is notoriously difficult to implement experimentally due to the generation of higher-order sidebands and optical loss, which limit the potential interaction distance. Here, we overcome this problem with an experimental technique that uses programmable phase and amplitude shaping to iterate the wave mixing initial conditions injected into an optical fiber. This extends the effective propagation distance by two orders of magnitude, allowing idealized Kerr-driven dynamics to be seen over 50 km of fiber using only one short fiber segment of 500 m. Our experiments reveal the full phase space topology, showing characteristic features of multiple Fermi–Pasta–Ulam recurrence, stationary wave existence, and the system separatrix representing the boundary between two distinct regimes of spatiotemporal evolution. Experiments are in excellent quantitative agreement with numerical solutions of the differential equation system describing the wave evolution. This experimental approach can be readily adapted to study other wave mixing and nonlinear propagation phenomena in optics.