Variations on a maze

By contrast, the maze output of 10 PRINT is oriented diagonally, giving it a distinctive visual look. Several things about this visual orientation are surprising. First, when we visually trace the maze the long runs or paths that lead through the maze do not follow the lines along which the maze is constructed (which remains left-right, top-bottom). Second, this is not an elaboration, but actually an elegant simplification that is part of the essence of the succinct one-liner. There are no two characters that, when substituted for our "\" and "/", will result in the construction of a traditional orthogonal maze. Vertical and horizontal bars result in a disconnected weave, while solid and empty squares result in rough static.

By contrast, the maze output of 10 PRINT is oriented diagonally, giving it a distinctive visual look. Several things about this visual orientation are surprising. First, when we visually trace the maze the long runs or paths that lead through the maze do not follow the lines along which the maze is constructed (which remains left-right, top-bottom). Second, this is not an elaboration, but actually an elegant simplification that is part of the essence of the succinct one-liner. There are no two characters that, when substituted for our "\" and "/", will result in the construction of a traditional orthogonal maze. Vertical and horizontal bars result in a disconnected weave, while solid and empty squares result in rough static.

As it turns out, diagonal mazes are symbolically efficient on a Cartesian grid due to the fact that four characters meet at the corners, whereas only two meet along an edge. Thus, intersections of up to four lines (the building blocks of a rectilinear maze) can be created at corners if we use diagonal lines.

As it turns out, diagonal mazes are symbolically efficient on a Cartesian grid due to the fact that four characters meet at the corners, whereas only two meet along an edge. Thus, intersections of up to four lines (the building blocks of a rectilinear maze) can be created at corners if we use diagonal lines.