Unitary evolutions of quantum lattice systems that preserve locality are called "quantum cellular automata," or QCAs. In previous talks at the summer school, we heard about the classification of QCAs in one dimension. However, physical systems usually require a more relaxed notion of "fuzzy" or approximate locality, because local Hamiltonian evolution is not a QCA in the traditional sense. In this talk, I discuss QCAs that satisfy a more relaxed notion of locality. We find that the classification of 1D QCAs is robust even when considering these more general evolutions. Based on work with Michael Walter and Freek Witteveen in arXiv:2012.00741.