SELF-AVOIDING CHIRAL WALKS

Abstract

We describe a simple, discrete model of deterministic chiral motion on a square lattice. The model is based on rotating walkers with trailing tails spanning L lattice bonds. These tail segments cannot overlap and their leading A segments cannot be crossed. As prescribed by their chirality, walkers must turn if possible, or go straight, or else correct earlier steps recursively. The resulting motion traces unbound trajectories and complex periodic orbits with various symmetries. Periods tend to decrease with increasing L and vary between L and L2. Interacting walkers can form intricate pair states. Some orbits match pinned spiral tip trajectories observed experimentally in excitable systems.