Turning machines: a simple algorithmic model for molecular robotics

Abstract Molecular robotics is challenging, so it seems best to keep simple. We consider an abstract molecular model based on simple folding instructions that execute asynchronously. Turning Machines are a 1D 2D model, also easily generalisable 3D folding. A Machine starts out as line of connected monomers in the discrete plane, each with associated turning number. monomer turns relative its neighbours, executing unit-distance translation drags other along it, and through collective motion initial set eventually folds into programmed shape. provide suite tools for reasoning about by fully characterising their ability rotations: almost-full rotation $$5\pi /3$$ 5 π / 3 radians possible, yet full $$2\pi$$ 2 impossible. Furthermore, rotations up executed efficiently, $$O(\log n)$$ O ( log n ) expected time our continuous Markov chain model. then show such line-rotations represent fundamental primitive using them efficiently asynchronously fold shapes. In particular, arbitrarily large zig-zag-rastered squares zig-zag paths foldable, y -monotone shapes albeit error (bounded perimeter length). Finally, we give despite having traverse all points, fact impossible fold, well techniques certain classes (scaled) without error. Our approach relies careful geometric-based analyses feats possible very robotic system, pushes conceptional hardness towards mathematical analysis away from implementation.