© Hindawi Publishing Corp. A CLASSIFICATION OF PERIODIC TURTLE SEQUENCES

Abstract

A turtle sequence is a word constructed from an alphabet of two letters: F, which represents the forward motion of a turtle in the plane, and L, which represents a counterclockwise turn. In this paper, we investigate such sequences and establish links between the combinatoric properties of words and the geometric properties of the curves they generate. In particular, we classify periodic turtle sequences in terms of their closure (or lack thereof). 2000 Mathematics Subject Classification: 68R01, 68R15. 1. Introduction. In [1