Anything based on graph traversal generalized trivially. And any maze-generation algorithm by definition will generate a spanning tree, so you can always post-process the generated trees to re-embed the graph in an arbitrary number of dimensions.
For https://github.com/gliese1337/M4ZE.js (a prototype 4D maze navigation game), I used a 4D specialization of Prim's algorithm. There is no time travel involved--it's just straight-up 4 fully equivalent spatial dimensions, with full 4D maneuverability and no privileged directions. At any given time, the maze is visualized as a 2D projection of a 3D hyperplanar slice through the maze, and one type of control action is to rotate your viewing hyperplane.
It is actually far easier to navigate than I initially thought it would be when I started working on it. I recently implemented a 4pi-steradian all-around view to make it a little bit easier, but the bump in navigation ease is minor (though I kept it because it's cool, and allows for tricks like running the maze entirely backwards). User testing so far indicates that kids and teenagers adapt to it quite quickly, while most adults have significantly more trouble.
For https://github.com/gliese1337/M4ZE.js (a prototype 4D maze navigation game), I used a 4D specialization of Prim's algorithm. There is no time travel involved--it's just straight-up 4 fully equivalent spatial dimensions, with full 4D maneuverability and no privileged directions. At any given time, the maze is visualized as a 2D projection of a 3D hyperplanar slice through the maze, and one type of control action is to rotate your viewing hyperplane.
It is actually far easier to navigate than I initially thought it would be when I started working on it. I recently implemented a 4pi-steradian all-around view to make it a little bit easier, but the bump in navigation ease is minor (though I kept it because it's cool, and allows for tricks like running the maze entirely backwards). User testing so far indicates that kids and teenagers adapt to it quite quickly, while most adults have significantly more trouble.