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We've been working on producing mazes by computer, with input from a human designer. We're interested in two complementary questions with respect to 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 aspec
The traveling salesman problem (TSP) is an old and well-studied problem in computer science. Given a collection of cities on a map, a salesman must make a tour of the cities, visiting each once, and returning to the city from which he started. Of all the ways that he could travel from city to city, he must find the one that requires him to travel the least total distance (our salesman is nothing i
Over his life, the Dutch graphic artist M.C. Escher created over a hundred ingenious tesselations in the plane. Some were simple and geometric, used as prototypes for more complex endeavors. But in most the tiles were recognizable animal forms such as birds, fish and reptiles. The definitive reference on Escher's divisions of the plane is Doris Schattschneider's Visions of Symmetry, now in a secon
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