In unsupervised learning, there is no obvious straightforward loss function which can capture the major factors of variations and similarities. Since natural systems have smooth dynamics, an opportunity is lost if an unsupervised loss function remains static during the training process. The absence of concrete supervision suggests that smooth complex dynamics should be integrated as a substitute to the classical static loss functions to better make use of the gradual and uncertain knowledge acquired through self-supervision. In this paper, we propose Dynamic Autoencoder (DynAE), a new model for deep clustering that allows to solve a clustering-reconstruction trade-off by gradually and smoothly eliminating the reconstruction objective in favor of a construction one while preserving the space topology. Experimental evaluations on benchmark datasets show that our approach achieves state-of-the-art results compared to all the other autoencoder-based clustering methods.