Mazes

Mazes are getting scientific! And yes that was an exclamation mark. The writers are interested in answering two fundamental questions about maze design.

Complexity: What makes a maze difficult to solve? The more we consider this question, the more elusive it becomes. It's certainly possible to begin defining mathematical measures of a maze's complexity, but complexity must depend on aspects of human perception as well. For example, the eye can easily become lost in a set of parallel passages. Complexity also depends on how the maze is to be solved. Are you looking down on the maze, solving it by eye? With a pencil? What if you're walking around inside the maze? And of course, complexity isn't necessarily what we want to measure. Ultimately we'd like to generate compelling puzzles, which may or may not have a high degree of complexity.

Aesthetics: How do we construct attractive mazes, particularly mazes that resemble real-world scenes? Here, maze design interacts with problems in non-photorealistic rendering. There are many great projects for producing line drawings from images. Our goal is similar, except that our lines must also contrive to have the geometry of a maze. This additional constraint affects how we think about creating a line drawing in the first place.