International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 34, Pages 2193-2201

A classification of periodic turtle sequences

J. Holdener and A. Wagaman

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

Received 11 September 2002

Copyright © 2003 J. Holdener and A. Wagaman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).