The maze one should not enter

Question

Once upon a time, somewhere in Italy, two archaeologists unearthed a buried passage.

As they explore the passage they reach the doorway which is clearly the entrance of a wide structure behind. They see well-built passages made of square stone walls. There are passage branching in various directions.

One of them exclaims:

-- It's a maze!

And indeed, it is. Very excited about their finding, they want to explore it. They start arguing about the best way to proceed without getting lost. But they stop when they see the following engraving on the wall.

-- Look at this, a map! Not much of a challenge. I'm a bit disappointed. What's the point of building a maze if you just put the full map at the entrance? That doesn't make any sense! Well, let's see what is at the other end.

The other doesn't reply, absorbed in his study of the engraving, scribbling on a notepad. Eventually he gasps and becomes pale.

-- That's not a map, it is a message. It is a warning!

-- A warning?

-- Yes, I know where this maze ends, and we definitely shouldn't go there!

From what you have seen and what you have read, can you tell me what the message says and where to the maze is leading?

Hint:

Forget steganography, hidden pixels or color filters. If you copy the maze on a notebook it should be good enough to solve it.

For reference:

╶─────────┬───┬───────────┬─────╮  
╷ ╶─────┬─┴─╴ ├─┬─╮ ╭───┬─┤ ╭─╮ │  
│ ╶─────┴───╮ ╵ ╵ ╵ ╰─╮ ╵ ╵ ╵ ╰─┤  
├─────┬─╴ ╷ ╵ ╶─────┬─┴─╴ ╭───╮ │  
├─╴ ╷ │ ╭─╯ ╶───┬─╴ ╵ ╭───┼─╴ ╵ │  
│ ╶─┼─┼─┤ ╶─┬─┬─┴─────╯ ╶─┴─╮ ╶─┤  
│ ╶─┤ ╵ │ ╷ ╵ ╰─╮ ╶─┬─╴ ╭───┴───┤  
│ ╶─╯ ╷ ╵ ╰─────┴─╴ │ ╶─┴─┬───╮ │  
├─────╯ ╶─────────┬─┴─┬───┴─╮ ╵ │  
│ ╶───┬───╮ ╭─╴ ╷ ╵ ╷ ╰───╮ ╰─╮ │  
│ ╶─╮ ╰─╴ ╰─┴─┬─┴───┤ ╶───┴─╴ ╵ │  
├─╴ │ ╭─────╴ │ ╷ ╷ ╵ ╶─────────╯  
╰───┴─┴───────┴─┴─┴─────────────╴  

Cont'd

-- A warning? What does it say?

The first archaeologist just shows his notepad. At the bottom you can see 3 lines of text, nicely aligned, 11 characters in width. The second one reads it and agrees.

-- If this is correct, we better get out of here.

Cont'd 1

-- But how did you even think it could be a message?

-- It is the ... well ... entropy of the map. There is no symmetry, no long corridors, the branching pattern is complex, there are way to many short dead ends. That is not how you build a maze. Looking at the map I could see that its complexity is uniform. I felt that the placement of each wall conveys hidden information.

-- I can't say I got that feeling. Is it so?

-- Yes. As I discovered, no wall is placed just randomly. Every single wall contributes to the message.

Cont'd 2

They are now on the surface, back to the car, eating a sandwich before hitting the road.

-- Funny the thing you told me earlier. I never realized that.

-- Which one? I am always funny.

-- Yeah, well... debatable. Anyway. It was about the pillars and the walls. That there are exactly as many pillars in a labyrinth as there are walls between the pillars.

-- That's true for every perfect maze. But that is not interesting. The interesting part is that one can match pillars to adjacent walls in a perfect one-to-one relationship. It is like one pillar with one wall form a unit.

-- Interesting... You give me an idea. If we want to go into the business of building prefabricated mazes, we just need to produce one type of piece, a pillar with an attached wall? That would work for every possible labyrinth? You never need an extra pillar or an extra wall?

-- Exactly. You still need to build the outer wall, of course.

-- We can subcontract that.

Epilogue

-- OK. There is still something I don't get. When you display a warning, you want to make it readable, right? Like bright yellow text on red background. What sense does it make to display it in such a cryptic way?

-- I can only guess that warning is a legal requirement. And they don't like it. So they found a loophole to comply without really complying.

-- They must have found the one lawyer who could think of such a thing.

-- I bet they are not short of that kind.

Answer 1

The message says "abandon all hope ye who enter here" which suggests that this maze leads to hell! (According to Dante's inferno which says that this messages is inscribed over the door to hell).

Here's how I got there. I needed all the hints and Steve's comments under the question were useful before I saw the latest hints.

First of all an annotated version of the maze:

My annotations are labels for each "pillar" of the maze saying whether its attached wall is horizontal or vertical. Green lines helped me to work out whether the wall was a horizontal or vertical...

Once I had 33 sets of 5 orientations (read top to bottom and then left to right) I changed those strings to binary numbers: h being 0 and v being 1. I then converted these binary numbers and used them as indexes into the alphabet. eg hhhhv = 00001 = 1 = a, hhhvh = 00010 = 2 = b, etc. 0 was a space and the ends of columns were also word breaks.

Answer 2

Although initially labelled conservatively as "A possible start towards a partial answer...", this turns out to actually have been the core of the actual answer, increased to more than 90% with the final comment, so I'll now undelete and "finish off" the part that had been posted as comments for easier access to how that answer was determined.

The hint marked "Cont'd" indicates that

we should generate a grid of 3 x 11 letters somehow.

I fairly quickly noticed that

ignoring the border, there are 15 x 11 interior nodes, which can be divided into groups of 5, making a 3 x 11 grid:

This would be the correct dimensions if

each group of 5 interior nodes and their pattern of connecting walls can somehow be converted into a character.

In principle, each of these boxes

could encode up to 10 bits of information on average, depending on which adjacent walls are present to each of the 5 interior nodes.

The later hint "Cont'd 1" seems to indicate that

there's about a constant entropy level within the grid, so a scheme along these lines, even if not divided exactly like that, may be the way to go.

The first (failed but suspiciously close) attempt was to

look at which "vertical" walls were present, and to use the binary code as an index to the alphabet. This resulted in:

   01   08   04    B    I    E
   02   15   15    C    P    P
   00   16   16    A    Q    Q
   05   01   05    F    B    F
   14   04   20    O    E    U
   14   24   02    O    Y    C
   11   05   08    L    F    I
   04   01   05    E    B    F
   00   02   18    A    C    S
   05   21   05    F    V    F
   08   08   00    I    I    A
   12   14   00    M    O    A 

It seemed "suspiciously close" because

all indexes were in the range 0-24 despite 0-31 being technically possible. At that point I tried various offsets (e.g. 0=A or 1=A or even 2=A), and got nowhere, so figured there was "something wrong" with the encoding.

I'd meant to look back more closely at the question for hidden clues about what to do next. Instead, "Cont'd 2" was posted, after which it was clear that

the directions of the walls "attached" to each node/pillar were important, so I recorded them:

 E E E E N W N E E E E E N E S
 E E E N W W N N N N W N N N E
 W W W W S N E E E E N W S W W
 W S N S W E E S W N E E S W N
 E E N W E E E E E E N E E S E
 E N N N S N N W E S W E E E E
 E N S N E E E N W S E N W W W
 W W W E E E E E E E E E N W N
 E E E E S S W S N S N W W N W
 E S N W E E S W W W E E N W N
 W S S W W W S S S N E E E E E 

This still left open

various ways to extract information from the groups of 5 pillars that still only really remained an "initial hunch" based on the first significant clue of 3 x 11 letters. Even if we're only considering a 5 bit code (which was far from certain at that point, I'd also wondered about other possible ways to have 8 bits encoded in the 10 raw bits available), which two directions should be considered "1" bits and which "0" bits, or is there some other encoding entirely? My first attempt was actually stupidly close, where "E" and "W" are interpreted as 0 bits, and "N" and "S" are interpreted as 1 bits...

   01   08   05    B    I    F
   02   15   14    C    P    O
   01   16   20    B    Q    U
   14   05   05    O    F    F
   04   00   18    E    A    S
   15   25   00    P    Z    A
   14   05   08    O    F    I
   00   00   05    A    A    F
   01   23   18    B    X    S
   12   08   05    M    I    F
   12   15   00    M    P    A 

However, I then tried different ways to extract a bit (resulting in different kinds of garbage) rather than trying something that would have easily let me see the actual message:

using 'A'-1 as the base rather than 'A'+0 resulting in:

   01   08   05    A    H    E
   02   15   14    B    O    N
   01   16   20    A    P    T
   14   05   05    N    E    E
   04   00   18    D    @    R
   15   25   00    O    Y    @
   14   05   08    N    E    H
   00   00   05    @    @    E
   01   23   18    A    W    R
   12   08   05    L    H    E
   12   15   00    L    O    @ 

Fortunately, @chris was able to see the step that I missed, and complete an answer before @florian-f got even more frustrated at how close I was getting in comments and then just missing the actual answer!

Answer 3

Partial answer:

This is the path through the maze. It is exactly 33 tiles long.

the tiles clearly correspond to the 33 characters.

I have considered various encodings based on each path tile being only one of four possibilities.

There are two ways I could encode - either the tile's entrance direction or its exit direction. Not much difference, the characters get shifted by one.

I have tried UDRL and NSWE, nothing interesting popped out.

I considered WASD as in the keys you would traverse the maze with but no.

I am wondering if DNA is somehow involved because it is also encoded with 4 different letters and commonly grouped in 3s as well! But I don't know which turns would correspond to which of ACTG.

Another possibility is that turns only navigate and don't have a meaning - the message characters are each tile's possible exits. This gives 16 possible values per character, 15 in practice as the "all closed" tile cannot be entered. I cannot begin bruteforcing the possible ways to assign these either.

All in all a hint may be in order, or someone else can use this to come to a better conclusion.