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

Spoiler alert

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

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

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

The orange highlight will disappear if you click the X.

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

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

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?

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.

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

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.

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.

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

Any maze with a wall that loops around itself.

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.

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.

More of a Labyrinth than a maze, since it has only a small number of very short dead-ends. The majority of the maze can be solved by simply picking a direction at at random, most paths eventually lead to the goal, just with varying lengths.

>A maze is a complex, branching (multicursal) puzzle that includes choices of path and direction, while a labyrinth is unicursal, i.e., has only a single, non-branching path, which leads to the center.

TIL

I live maybe 20-25 minutes walk from here and never heard of this

Not free, but not a short walk from where I live is the Hampton Court maze, which is the oldest hedge maze in Britain:

https://en.wikipedia.org/wiki/Hampton_Court_Maze

And the biggest is at Longleat, where my wife’s job is to rescue people with a megaphone when they get lost. She also has to go hunting for a surprisingly large number of lost phones.

Oh wow, I did not know about this one. It looks like the advanced maze for expert users. Pro, paid version.

that is very neat, I will try to check this out next time I am in London

There's another great maze in London called "Zone 1", many tourists and locals get completely lost in there every day

There are loads of gaps which pretty much ruin the maze. The photos here have been very kind. It's really not worth a trip, I'm saying that as someone who lives 10 mins away and has kids. However, the tiny zoo there is a good visit.

You know you don't need to use the gaps, right?

Please come and explain that to my young daughter. Some of the gaps are now arguably new pathways and it's all over in a couple of mins. For everyone else, save yourself the trip.