A particular class of irreducible representations of Leavitt path algebras were defined by Chen in 2013. These representations have since been generalized, but until recently these (as well as projective modules based at sinks) were the only known irreducible Leavitt path algebra modules. In this talk we will discuss non-Chen irreducible representations of Leavitt path algebras, as well some background material in symbolic dynamics. This is joint work with Murad Ozaydin.