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