Fig. 2.

Turning Machine model. a Triangular grid conventions. A configuration showing a single monomer on the triangular grid $G_{▵}$, along with axes x, y and w. b Local movement (rotation): A monomer in state 3 pointing to the east undergoes three turning rule applications finishing in state 0 with no more applicable rules. Locally, the monomer effects a rotation motion. c Global movement (translation): Left: Example initial configuration. Middle: A movement rule applied to a monomer in state 3 decrements the state to 2 and translates all subsequent monomers by $+\overrightarrow{w}$. Right: A second state-3 monomer moves. d Blocking: Monomers are not permitted to make movements that would result in a self-intersecting configuration. The monomer $m_j$ is said to be blocked because if it were to move, then $m_k$ would move to overlap $m_i$, but such self-intersections are not permitted