Three-sheet Weaves, Knots, Braids, and Mazes


Throughout college, I used to doodle the pattern in the interior of the first image below and in the background image on this page as a weave of three interlocking (Borromean) sheets. In the following years, I steadily started mixing in connections between the sheets and eventually hit on the idea of using it as the basis for creating mazes.

Around new year's of 2001, I wrote an OpenGL program that gave me an interactive editor for laying out the designs using OpenGL's transparency to show the overlaps and its color blending to distinguish between the three sheets. The editor gives me a large workspace of hexagons which I can scale and translate using the right mouse button and a gestural interface for creating the paths using the left mouse button.

I created the images below by hand using the editor. In the future, I'd like to revisit the program to add automatic maze generation by having it automatically fill in paths through groups of cells selected by the user. This page has a start at exploring maze generating algorithms.



This final image is a POV-Ray rendering of a 3D geometry of the three sheets.



This page made possible by Dollins Investment Advisors, LLC.

Steven C. Dollins
Last modified: Sat Nov 19 14:42:15 PST 2005