Playful Mathematician Creates Toroid Mazes

November 17, 2009

Russ Lyons (Indiana University) likes to create three-dimensional toroid mazes and delve into their mathematical properties for fun.

"There are a huge number of these mazes that can be made, and a very simple algorithm can create each maze," said Lyons.

Lyons wraps a two-dimensional maze into a cylinder and then connects the edges. The resulting "donut maze" reveals some interesting properties and puzzles.

Every point on the resulting maze can be reached from another point and only one path connects any two points. Additionally, in Lyons' mazes, a unique set of edges traverses any donut in any direction. You can go around any one of his donut mazes innumerable times without backtracking.

 Lyons enjoys the challenge of solving the mazes and his hobby has developed several questions that merit further study. For instance, it is unclear how many edges actually span the mazes when they are randomly generated.

"There have been plenty of important, historical discoveries that were discovered by basic research out of intellectual curiosity, and not practical concerns," said Lyons. "And besides, it's fun."

Source: IU News Room, November 9, 2009.