We investigate the novel properties of optical fiber lines made of Mamyshev regenerators (MRs) based on self-phase modulation and subsequent spectral filtering. In particular, we show that such a regenerator line can be used to generate random sequences of optical pulses from an incoherent wave. This behavior is related to the existence of stable eigenpulses that can propagate unchanged through the regenerator line and act as attractors for incoming pulses. By changing the regenerator parameters, we also report the existence of multiple eigenpulses and limit cycles. Finally, we demonstrate that MRs could be used as efficient nonlinear gates in fiber laser cavities.