AbstractWe investigate computability of a self‐similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self‐similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self‐similar set is a recursive compact set. A further result on the case that the self‐similar set forms a curve is also di