The generation of all paths from a given lattice point to another one is considered. The paths are constrained within the limits of a rectangle and are described by unit steps in orthogonal directions. The paths follow a prescribed number of self-intersections and a given length. Several particular cases extend the basic problem. Paths that do not leave holes, i.e., paths that touch each of the square forming the underlying grid are generated.
Some paths can give rise to fractals.
The file paths.gz is a compressed file containing the notebook paths.nb.