we say that a finitely generated group is self-simulable if every action of the group on a zero-dimensional space which is effectively closed (this means it can be described by a turing machine in a specific way) is the topological factor of a subshift of finite type on said group. even though this seems like a property which is very hard to satisfy, we will show that these groups do exist and that their class is stable under commensurability and quasi-isometries of finitely presented groups. we shall present several examples of well-known groups which are self-simulable, such as thompson's v and higher-dimensional general linear groups. we shall also show that thompson's group f satisfies the property if and only if it is non-amenable, therefore giving a computability characterization of this well-known open problem. joint work with mathieu sablik and ville salo.