A set \(M \subseteq \mathbb {R}^2\) is a Moser set if for every worm \(w\) of unit length there exists a direct isometry \(\varphi \) with \(\varphi (w) \subseteq M\).

Given a finite list of candidate worms \(W\) and a finite list of isometries \(I\), a set \(M\) is a \((W, I)\)-approximate Moser set if for every \(w \in W\) there exists \(\varphi \in I\) with \(\varphi (w) \subseteq M\).