Visual Representation of Periodicity in Partial Words

This applet builds two- and three-dimensional representations out of a partial word based on two of its weak periods. Isolation will be visible if it occurs within the word. In the 2D version, the array will be repeated to show where the top of the array should connect with the bottom.

Type 1 isolation occurs at the beginning of the word; the subset will be isolated on the right and the bottom.
Type 2 isolation occurs in the middle of the word; the subset will be isolated on all four sides.
Type 3 isolation occurs at the end of the word; the subset will be isolated on the left and the top.

This applet uses Java Technology, and requires the JRE 5.0 and Java 3D for Windows (DirectX Version) Runtime for the JRE.

The 3D version will open in a new window. Holding the left mouse-button down and dragging the object will cause it to rotate. The right mouse-button controls translation. Alt-clicking or using the middle button will allow you to zoom in or out on the object.

Color key: a b c d e f g h i j k l m n o p q r s t u v w x y z

Acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. DMS-0452020.

Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.