Mazes

What’s the difference between a maze and a labyrinth?

It is generally accepted that a labyrinth contains only one path, which often spirals around folding back in on itself in ever-decreasing loops. On the other hand, a maze contains branching paths, which lead to nowhere, and therefore present the person with choices and the potential for them to get lost.

Mathematicians have created maze-generating algorithms, which tend to fall into two main types:

  • Ones that start with a single bounded space and then sub-divide it with walls to produce smaller sub-spaces;
  • Ones that start with a bunch of disconnected rooms and then demolish walls to create paths between them.

Escaping Mazes

Most methods work for ‘simple mazes’, i.e. mazes with no short-cuts via bridges or passage loops (circular paths that lead back to where they started).

So, if we assume the maze is simple, the most common method to escape the maze is wall-following. Here, you place a hand on the wall of the maze, keep walking maintaining contact with the wall and eventually you will get out.

Why does this work? If you imagine picking the wall of the maze and stretching its perimeter to remove any corners. You will eventually create a circle-like shape, which must form part of the maze’s outer border.

Trémaux’s Algorithm

The problem is that most mazes aren’t simple, for example the Escot Gardens’ beech hedge maze in Devon.

Beech Hedge Maze in Devon | lotstodo.co.uk

So, another method of maze escape is known as Trémaux’s algorithm, which works is all cases.

Here’s how it works. Basically, with this algorithm, you leave a trail as you navigate your way through the maze. Then follow these rules:

  • If you arrive at a junction you have not previously encountered, randomly select a way to go;
  • If that leads you to a junction where one path is new but the other is not, select the path you have not been on;
  • If you are choosing between a once or twice-used path, choose the path that has only be used once, then leave a second trail behind you;
  • Never select a path that already has two trails.

This method works for all mazes and is guaranteed to get you out!

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