## ABSTRACT

In this paper, we prove that a wide family of origami maze designs can be folded with a small scale factor. We develop an algorithm to fold a square of paper into any orthogonal maze, consisting of vertical walls protruding equal heights out of a square ﬂoor. More precisely, given an orthogonal graph drawn on an n×n square grid, we fold a (2h+1)n×(2h+1)n square of paper into the square with the orthogonal graph extruded orthogonally to a speciﬁed (uniform) height h. The zero-thickness ridges could form a path like the Hilbert curve, a maze or labyrinth, troughs for liquid distribution, or letters of the alphabet (as in Figure 1).