Reconfigurable systems and the Fibonacci snake

Reconfigurable systems are used to model real-world (and mathematical) situations that have reversible movements between states. The possible states of a reconfigurable system can naturally be visualized cubical complex. When situations are thought of in this manner, it becomes possible to pose questions of optimization in terms of geodesics in cubical complexes. CAT(O) cubical complexes will have unique geodesics between any two states; but thus far, very few examples of re-configurable systems with CAT(O) cubical complexes have been found. We provide a class of reconfigurable systems whose complex will always be CAT(O). We build on the techniques of Ardila-Owen-Sullivant, Baker, and Ghrist-Peterson for using combinatorial methods to prove that a given complex is CAT(O)