Research suggests that the texts produced using machine translation (MT) do not fully represent the linguistic traits of the natural language. Yet, the ever-increasing quality and access to MT is resulting in its steady adoption by both language professionals and general users. According to contact linguistic theories, such adoption might result in MT-specific language traits permeating the target languages. This work takes a first step into considering the changes that a language might endure over time by observing the variation of linguistic trends along a series of MT generations. We train ten sequential engines using each to produce the target side of the training corpus of the following and calculate a number of metrics to observe linguistic diversity at a lexical, morphological, and syntactic level for a large, fixed test set. Quantitative results show an initial loss of lexical diversity, which, albeit gradually, only continues at a much slower pace in the following MT generations. In turn, structural variations and, in particular, morphological variations across generations are less marked, which might indicate a more stable behaviour regarding grammatical consistency. Overall, the resulting MT language seems increasingly homogeneous, marked by the reduced presence or disappearance of low-frequency words, and compact, with a decreasing proportion of function words relative to content words.