Maze Types and Topology: A Summary

Ever wonder what kinds of mazes are out there to confuse you? Most common mazes fall into several basic categories. If you know the type of maze you are facing, this could affect your maze-solving strategy. Here are the basic types of mazes:

Maze puzzle of the Parthenon, Athens (438 BC)

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Arrow Maze: A type of logic maze containing some passages that may only be followed in one direction (denoted by the arrows). The arrow maze is something called a "directed graph" in mathematical terms, and it is the fundamental type of maze to which almost every other maze type can be reduced (with enough exotic transformations).
Block maze: A maze that cannot be solved without clearing the maze pathways of moveable blocks. When well-designed even very small block mazes can be complex to solve.
Logic maze: A maze that must be navigated by adhering to logical rules in addition to following its passages. Examples might include a maze containing different colored symbols that must be passed in a certain order, or a maze that has some passages that may only be followed in one direction (an arrow maze).
Multicursal maze: A maze with at least one junction (or node), and thus having more than one path.
Multiply-connected maze: A multiply-connected maze contains one or more passages that loop back into other passages, rather than leading to dead ends. A well-designed multiply-connected maze is more difficult to solve than a simply-connected maze, for users will spend a great deal of time simply going around in circles. The extreme multiply-connected maze has no dead ends at all, and is called a "Braid maze." The Amazeing Art mazes are multiply-connected mazes.
Number Maze: Any maze that uses numbers (or letters, symbols, etc.) by which the maze solver can jump to other areas in the maze by following the numbers, avoiding the usual walls. For example, a number maze with the letter "A" in two places would allow you to jump from one "A" to the other. Because of these jump connections, such mazes are partial weave mazes.
Planair maze: A mind-bending maze whose underlying topology is unusual (non-Euclidean) and which has edges that connect with one another. For example, mazes covering the surface of a torus or a Moebius strip would be planair mazes.
Simply-connected maze: Simply-connected mazes have pathways that never re-connect with one another, so every path you choose either leads to additional paths (a fork) or to a dead end. There is only one solution to a simply-connected maze, and it can always be found by following the "left hand rule "—simply walk forward, keeping your left hand on the wall at all times.
Weave maze: A weave maze has pathways that go under and over each other. Though often drawn on paper, it in fact exists in more than two dimensions and can easily foil some common maze-solving tricks and techniques. An outdoor maze that has bridges or tunnels is a partial weave maze.
Unicursal maze: A maze with a single path (commonly called a labyrinth).

Most modern maze makers create either multiply-connected, weave or logic mazes. Many mazes are a combination of types. For example, quite a few outdoor mazes are multiply-connected weave mazes, because they have passages that connect back and forth as well as passages that go over or under other passages (via bridges, tunnels, etc.). Computer-generated mazes can be of any type, but the printable kind are usually simply-connected mazes.

Dole Pineapple Plantation Maze

Mazes and Labyrinths — the differences

What is the difference between a maze and a labyrinth? Most people today think of a labyrinth—such as the one at Grace Cathedral in San Francisco—as something with a single path that winds into the center. To get back out you simply have to retrace your path.

In contrast, a maze is a left-brain puzzle, often with false passages, many choices, and dead ends. Whether it is on a piece of paper or outdoors—like the enormous Dole Pineapple Plantation maze in Hawaii—you can get lost and confused in a maze.

The idea that labyrinths have a single path arose only in the last century. In the ancient world, a labyrinth was an inextricable construction that was chaotic and confusing for those trapped within it. Theseus, after all, got lost in a labyrinth and needed a golden thread to find his way out. Unless he was quite dimwitted, he was exploring what we would today call a maze.

To those able to see its pattern from afar an ancient labyrinth also revealed its order and artistry. It was a place of planned chaos where the labyrinth designer attempted to outwit the labyrinth explorer. The mysterious Egyptian Labyrinth is a famous example of an ancient labyrinth.

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A simply-connected maze has pathways that never re-connect with one another, so every path either leads to additional paths (a fork) or to a dead end.

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Maze Types and Topology: A Summary

Mazes and Labyrinths — the differences

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