On: Even Been to This Free London Yew Maze?

[tromp]

A map of the Millenium Maze: https://i.etsystatic.com/33392302/r/il/e40c9a/3604868640/il_...

[OscarCunningham → tromp]

Ah, a maze where the 'left-hand rule' doesn't help.

[PartiallyTyped → OscarCunningham]

What kind of structure do mazes where the left-hand rule doesn't help have?

From a first glance, cycles, but is it really a maze without those?

[LeoPanthera → PartiallyTyped]

A maze where the goal is not on the edge of the maze. In this case, the goal is in the center.

3-dimensional mazes (which have bridges or tunnels) also often cannot be solved with this rule.

[zvr → LeoPanthera]

You first statement is not correct. The rule is perfectly useful to solve mazes where the goal is in the center.

The requirement is that the walls should be connected, i.e. that there are no free-standing walls somewhere in the maze not connected to the border walls, for example.

[LeoPanthera → zvr]

I stand corrected! I suppose it is possible to have a center goal that is connected to the edge by a wall.

[Shared404 → PartiallyTyped]

The left hand rule assumes that the end is on the same "cycle" as the entrance:

   --E--
  |     |
  |     |
   --S--

if the end is instead on a different "cycle", it won't work:

   -------
  |       |
  | -- -- |
  ||     ||
  ||  E  ||
  | ----- |
  |       |
   ---S---

Hopefully this makes sense. I'm sure there's a propper phrasing of this in topology, but I don't know it.

[kfixjviv → Shared404]

"Multiply connected" is the topological term used in the English-language literature on mazes.

[OscarCunningham → PartiallyTyped]

Yes, in a maze without cycles the left-hand rule will take you through every part of the maze, guaranteeing that you reach the goal.

Of course in a maze with cycles you might still reach the goal, but it's not guaranteed. For example there's a cycle in Hampton Court Maze, but the left- and right-hand rules both get you to the goal from the entrance.

[curiousgal → PartiallyTyped]

Any maze with a wall that loops around itself.

[kfixjviv → PartiallyTyped]

They are referred to as "multiply connected" in the literature on mazes. Essentially, this is the mathematical way of saying that there are "islands" of hedge, not attached to the perimeter.

[teekert → OscarCunningham]

Oh no! Guess we need a slime mold to solve it.

[pimlottc → tromp]

Spoiler alert

[tuukkah → pimlottc]

Also mapped on OSM with the name Millennium Maze: https://www.openstreetmap.org/way/4940708

[tromp → tuukkah]

Nice, but they could have used some more contrasting color for the maze paths...

[tuukkah → tromp]

The orange highlight will disappear if you click the X.

Also, if the hedges were mapped, they would appear in dark green on the map.

[LeoPanthera → tromp]

"OSM" is just data. You can supply your own renderer.