
*** maze ***

In this example the homology of a closed maze stored in a bitmap file 
is computed. The external wall forms the circle in which the maze is
contained. If the maze picture has the homology of the circle, 
then this means that all the internal walls can be homotopically 
contracted towards the external wall and, as a consequence, from 
every place inside the maze to every other place there exists 
a path between the walls and this path is unique.

First, the black pixels in the picture are extracted to form a cubical set 
- in this case, a set of squares. For this purpose the program "bmp2pset" 
is used. This program converts a bitmap picture to a set of points in R^2 
corresponding to lower left corners of black pixels in the picture. 
Then the homology module of the resulting set is computed by the program 
"homcubes". Note that before the algebraic computations are performed, 
the set of cubes (or rather: squares) is reduced: cubes which can be 
removed without change to the homology are deleted from the cubical set.

WARNING: The set of cubes may be quite large - about 400 kB of disk space!
