Turning Machines

Authors Irina Kostitsyna, Cai Wood, Damien Woods

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Author Details

Irina Kostitsyna
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Cai Wood
  • Hamilton Institute and Department of Theoretical Physics, Maynooth University, Ireland
Damien Woods
  • Hamilton Institute and Department of Computer Science, Maynooth University, Ireland


We thank Vera Sacristán and Suneeta Ramaswami for insightful ideas and important input. This work began at the 29th Bellairs Winter Workshop on Computational Geometry (March 21-28, 2014 in Holetown, Barbados), we thank Erik Demaine for organising a wonderful workshop and providing valuable feedback, and the rest of the participants for providing a stimulating environment. We also thank Dave Doty and Nicolas Schabanel for helpful comments.

Cite AsGet BibTex

Irina Kostitsyna, Cai Wood, and Damien Woods. Turning Machines. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We fully characterise the ability of Turning Machines to execute line rotations, and to do so efficiently: computing an almost-full line rotation of 5π/3 radians is possible, yet a full 2π rotation is impossible. We show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold arbitrarily large zig-zag-rastered squares and y-monotone shapes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • model of computation
  • molecular robotics
  • self-assembly
  • nubot
  • reconfiguration


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