International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 34, Pages 2193-2201
doi:10.1155/S0161171203209078

A classification of periodic turtle sequences

J. Holdener and A. Wagaman

Department of Mathematics, Kenyon College, Gambier 43022, OH, USA

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).