Mortin Myes' Second Cryptic Gallery

Despite finding Mortin Myes' First Cryptic Gallery fairly simple to decipher, I must confess that his second one had me completely stumped.
Once again, there were three paintings, and this cryptic gallery was given the rather enigmatic subtitle 'Evolution of Maze'.

Keeping in with the theme of the first cryptic gallery, the first two paintings were fairly similar in content (indeed, the second painting was a very logical evolution of the first!), with the last being entirely unexplainable. The final painting was just a four digit number, nothing else.

I rung up Mortin today to give him the answer to his Baffling Birdcage Puzzle, and then took the opportunity to ask if 'Evolution of Maze' maybe needed more information, perhaps in some other cryptic gallery of his, but he assured me that each gallery was it's self contained puzzle.

I shamefully admitted defeat and Mortin gave the answer to me. He was actually a bit apologetic: 'I could've made the evolution of the maze much clearer! I mean, a few extra paintings, and colours would definitely have helped. But when you know how it works, it's quite simple, isn't it?'

Below I've provided my replication of the first painting in the gallery. The second painting in the gallery is simply the same maze, topologically, everything is the same apart from one minor aesthetic difference. I'll provide the second painting if the going gets rough!

My puzzle to you is: can you work out what 4 digit number this maze really represents?
It's a doozy. Give a shout if you need help!

EDIT: I would like to add, despite the steganography tag, there is nothing 'hidden' in the image. There's no tiny details to decipher. Additionally, you will have 0 doubts that you have solved the puzzle when you find the correct answer.

All text is possible to encode using Mortin's maze method.

Once you know Mortin's method, you could read a similar maze in just a few seconds.

• Shameless plugs to my other puzzles included in the ramble, but they're not linked to this puzzle whatsoever. Also, this puzzle can be solved entirely with just the picture and the fact that it becomes a 4 digit number. All the other stuff is just hints, because I consider this puzzle very difficult. Dec 16 '16 at 12:49
• 0 doubts? Not no/zero doubts? Hmmm :) Dec 16 '16 at 12:56
• @Techidiot unfortunately that's not a clue! :) Most of the text in my puzzles is just fluff. Usually, if anything is a hint (that isn't necessary to solve the puzzle, just might make it easier), it'll be dialogue from Mortin. Dec 16 '16 at 12:58
• Oh. Forgot to upvote. +1 :) Dec 16 '16 at 13:01
• 1000? Reading upward on the diagonal I can almost make out the letters T H O U S A N D. More seriously, do you take requests? What would 1000 look lke? (Very artistic effect by the way. Reminds me of an oblique bird's-eye view of mesa-topped canyonlands.)
– humn
Dec 17 '16 at 3:34

It’s as if the mystery number were spelled out in crayon on the backing of the frame. (It isn’t, but might look like this, demonstrating that care must have gone into getting the real picture to be so mazey.)

Evolution of $\scriptsize\raise-1ex\rlap\wedge\kern.1em$a Solution: a lesson in $\scriptsize\raise-1ex\rlap\wedge$ lateral   diagonal vertical thinking

Stage 1. Goodbye, vertical thinking. Hello, “lateral” thinking. Detect a number, barely.

LeppyR64 and powersupply presented valuable art critiques and puzzle-poser TheGreatEscaper commented/hinted that the underlying portrayal system is directly graphical.

LeppyR64 made a 180° overlay that reinforces the regularity of vertical bars and powersupply pointed out how much information is redundant, all of which leads to a focus on horizontal (lateral) bars/gaps and to a disregard of vertical bars. Looks like the mystery number is 5039.

Stage 2. Hello, diagonal thinking.

The digits can be recognized much more clearly with a possible evolution of components from horizontal to diagonal to invisible.

Perhaps vertical bars have something to say after all, as diagonals creep along them into place.

This became crystal clear from M Oehm’s insight that deserves a post of its own but has generously been donated to this one.

“I think you could overlay a diamond grid over the maze, so that the nodes of that grid are the midpoints of the vertical walls. Then use only the segments in that grid that cross a gap: Like this. That also explains why there are no adjoining vertical walls: The grid is like a checkerboard and only every other cell has a node.”   – M Oehm

Couldn’t resist depicting an interpretation beneath that “like this” image.

Stage 3. welcome back, vertical thinking!

By combining the above progress with poser’s revelations in Not Quite Wrap-up: The Half-Making Of Mortin Myes’ Second Cryptic Gallery, we can see how the pertinent information is completely vertical after all. We can also see how the interpretation so far would be half stymied by a minor change in one secret digit.

The painting’s maze walls are better understood as being thicker while corridors become thinner to match. Those horizontal gaps attended earlier are now vertical passages. A diagonal grid thus has each diamond/square being crossed either horizontally or vertically, by either a wall or a corridor. All vertical crossings, of either kind, become highlighted pixels.

Check marks ($\small\checkmark$) denote gaps that were interpreted successfully so far. Question marks (?) denote gaps that would have failed to be understood if digit 3 were rendered slightly differently.

Commemorative postcard

• Niiiiiice! That's definitely the number, although I'll say that your 'reading' of the maze is somewhat half-complete... Dec 17 '16 at 9:43
• there's only this one layer to the puzzle, so you have solved all there is to be done here, I'll just say there are ways to make the numbers EVEN more clear. Dec 17 '16 at 9:49
• Ah, very good! I think you could overlay a diamond grid over the maze, so that the nodes of that grid are the midpoints of the vertical walls. Then use only the segments in that grid that cross a gap: Like this. That also explains why there are no adjoining vertical walls: The grid is like a checkerboard and only every oter cell has a node. Dec 17 '16 at 11:23
• Would be fascinating to include a work sketch, @TheGreatEscaper (if that is your real name,,, Mortin?)! One of the most valuable aspects of this site is sharing how puzzles are made. This (or a wiki?) answer could be like a side exhibit in MM's gallery.
– humn
Dec 17 '16 at 11:54
• Artistic Answer! +1 Though, I had a little bit of Déjà vu here :) Dec 21 '16 at 13:13

Some detailed images for anyone who wants to look at them. I have offset the layers slightly for visibility. If anyone wants me to update it in any way let me know.

0 and 90:

0 and 180:

0 and 270:

All Four:

• Interesting idea, but I think before any experimentation should happen, you should sit back and have a look at the picture. Dec 16 '16 at 15:09
• One of these overlays helped solve the puzzle, by the way, with attribution. Thank you, LeppyR64!
– humn
Dec 19 '16 at 8:10

This is either a partial solution or an embarrasing attempt.

Hidden in the maze ...

is the number 222:

Unfortunately, 222 isn't a four-digit number, but without rotations I can't find any other hidden numbers. (There's a rotated 7 in the north-east corner. It stands alone, but the 2's are embedded in the maze's walls and if we allow that, a rotated maze has way too many 1's and 7's. Besides, where does the 7 go in the final number? Is it 7222, 2722, 2272 or 2227? So if my solution is heading in the right direction, I suspect to find a fourth 2.

Rationale and musings:

The numbers I found use the 7-segment numbers of calculator and alarm-clock displays:

Looking for patterns in the maze's walls seems a bit haphazard, but the maze is special: It has no enclosures, which rules out 0, 6, 8 and 9. More importantly, it doesn't have two north-south walls in a straight line, which rules out all digits except 2 and 5. So in this particular maze, highlighting the 7-segment numbers seems okay.

Finally, the position of the numbers could mean that the number is 22² (which is 484, so it's still one digit short) or 2²² when the maze is mirrored vertically (but that's too many digits) or even 2 − 2², when the wall between the lower 2's is considered a minus sign, but that's −2.

Finally, the OP's remark in a comment to another answer that we "should sit back and have a look at the picture" first seems to back up this simple solution.

• Dear M Oehm, I think your diamond/checkerboard insight belongs here. Go ahead, reclaim and delete it from my post any time (but I'll still attribute you for clarifying the picture way beyond my suspicions). The postcard follow-up puzzle is specifically in your honor, by the way..
– humn
Dec 19 '16 at 8:06
• @humn: Oh, I think my checkerboard comment makes sense only in the context of your solution. If you hadn't presented the idea to mark the horizontal gaps I'd never seen the pattern. I'll leave this answer as it is to document my failure to read between the lines. Dec 19 '16 at 17:50
• I like the postcard puzzle, and I can also see three fives in the horizontal zipper line. Dec 19 '16 at 17:50
• Good eye once again! I hadn't noticed those 5s,,, or all the Zs . . .
– humn
Dec 19 '16 at 20:46
• Once you've detected a pattern, you can see it everywhere! Everywhere! Dec 19 '16 at 20:51

Not Quite Wrap-up: The Half-Making Of Mortin Myes' Second Cryptic Gallery

This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community.

Caution: This post may contain spoilers.

Inspiration

I was playing around with binary pixel effects (i.e. if a pixel is 'on', turn it into some sort of pattern, and if a pixel is 'off', turn it into another. The typical one used everywhere, is 'on' is a black square, and 'off' is a white square!) and came across something particularly interesting. Now, the effect that I came across is actually a bit more difficult to decipher than what exactly has been presented in this puzzle, so I won't elaborate on it too much unspoilered here, but suffice to say it was the inspiration for this puzzle :)

Evolution

Well, upon finding the aforementioned effect, my first instinct was not to make a puzzle, but instead an encryption method. With a few random thoughts, I was able to create (what is in my opinion) a very very very difficult to crack encryption method for any sort of information at all, turning any message, textual or pictorial, into a sequence of 0s, 1s, 2s, and 3s... but that's a story for another day.
Anyhow, the purpose of an encryption is to essentially be an impossible puzzle, and puzzling.se is not a place for impossible puzzles. So, I backtracked a bit, back to the initial pixel effect. I decided to add one more layer to the pictorial encryption, and had to pick what to encode. In the end, I decided on numbers - there's something special about pixel numbers that makes this puzzle just a little bit easier.
What I failed to realise at the time is that same something special about pixel numbers also means that half of the encryption gets lost! If anyone remembers being around in the Sphinx's Lair, I realised this a few minutes in and said 'This actually might not be as difficult as I thought...' Thankfully, the difficulty seemed to be enough to keep some puzzlers occupied for a while :)

Anyhow, what has been discovered in this thread - and all of what can be discovered from this particular puzzle - is not actually the entirety of my intended encryption method. It certainly works for four digit numbers, and it's a perfectly acceptable solution to this puzzle from Mortin...
But for the curious puzzler, I'll pose a secondary challenge:

What on earth is THIS supposed to be?!?!?!?!?

Mortin's second painting

Pictured above is Mortin's second painting. As you can see, topologically identical to his first. But this painting provides crucial information that will explain the mysterious challenge above.

The process of making a Mortin Maze

Alright, so this is where we get into TRUE spoiler territory. If you've not yet attempted the secondary challenge, I'd highly recommend spending at least a few minutes on that before you read the following spoilers!!!

It's a pixel image! Once you've made a pixel image (in this case 5039), just make a lot of empty space around it. (Hey hey, arbitrary information)

THIS is the pixel effect. Are things starting to make sense?
Experiment a bit with making small pixel images and applying this effect. Maybe this is even enough information to solve the mysterious second challenge!

Above is what you get when you apply the effect to '5039'. Doesn't quite look like the painting in my question, does it? Because the information in this image can actually be simplified.
(Exercise to reader: Prove that up to this step, any Mortin Maze can be coloured in two colours such that no adjacent areas are the same colour!)

Above is how to simplify the information, by colouring in!

And if you 'unthicken' each coloured in section, you end up with the painting in my original question :)

How to DECODE a Mortin Maze

So maybe you're dying to know what the mysterious second challenge is. Maybe you're happy enough that you solved my original question! But to see the full extent of Mortin's encryption system, feel free to read the spoilers below.

Our mysterious second challenge, unedited.

Our mysterious second challenge, thickened. I wonder what the colours I've put in mean?

Our mysterious second challenge, thickened, and with a focus on verticals and horizontal lines. You can probably see what this is going to be now!

The next step is the hardest, it's identifying the RESULTS of the pixel effect.

Identifying the pairs of parallel lines next to each other gives this.

So our original pixel image was in fact:

Wowee! That looks familiar. But hopefully these pictures make it clear that the Mortin Maze encryption system is in fact much more versatile than the example I chose to pose to puzzling.se makes it out to be!

Final Thoughts

In trying not to make the puzzle too hard, I actually lost a bit of my encryption system. Hopefully it was still fun and difficult enough nonetheless, and consider the full encryption system a bit of an interesting easter egg :)

• This is looking like another healthy serving of visual interest! Thinking pixels instead of diagonals, and reading no further, the secondary challenge is already presenting a symmetrically calming likeness of pasta. Could it be? Wouldn't want to read further if I'm on the wrong spiritual path.
– humn
Dec 19 '16 at 22:35
• You're on the right spiritual path :) Although I can't say that the critter is quite the one you're thinking of... but you're getting the hang of reading a Mortin Maze, definitely!! Dec 19 '16 at 22:52
• This write-up inspired a new picture to work into my solution. Should've been thinking vertically all along.
– humn
Dec 20 '16 at 14:16
• Wow, what a great picture! It's so awesome that you made that, it's really clear :) Dec 20 '16 at 15:00
• Mortin's secret number is just to produce a maze which didn't reveal it's secrets too obviously :) The puzzle is done, my friend! I hope you had a good time with it! I know I very much enjoyed reading your progress and your wonderfully diagrammed solution. Dec 21 '16 at 13:18

my attempt & solution: (sorry for mad paint skillz)

process (hint, no spoiler)

1) mask out all redundant information

solution

2) count the number of line segments in each cluster

my stumps

I really wanted that thing up top to resolve to a seven, and the thing in the middle a 3. So the intuitive solution for me would be 1 3 4 7. can't justify it though.

extra thoughts

the 1 could potentially be a 2

• Your skillz helped solve the puzzle, powersupply, and have been attributed. Thank you!
– humn
Dec 19 '16 at 8:09

Though this may not be even close and way off the track, but was tempted to post an answer :) -

I think the number is -

3241 using the method of finding unique path lengths hidden inside the maze.

First Digit

If we try finding the individual paths formed inside the maze and draw a tree structure out of it we get this -

So, the first path starts from Black and ends with Orange and Purple which gives the following tree diagram

Hence, the length of this tree is 3 which means the first digit is 3

Second Digit

Second path is just under the first. Starts with Black and Ends with Green and Yellow.

The tree for the same is -

The length of this tree is 2 and hence the second digit is 2

Third digit

The next path is at the bottom which starts with Black and Ends with Pink and Purple.

Related tree diagram looks like this-

The length of this tree is 4 and hence the third digit is 4

Fourth Digit

Assuming all other paths are of the same size which is 1, I will consider the next number as 1

• Not quite... The tree graphs are a bit arbitrary aren't they. The answer will be very obvious when you've found it! Are there any interesting aspects to how the maze looks? Dec 16 '16 at 13:37
• -1: There's no reason that the 0 should come at the end rather than anywhere else, and it's unclear how you formed the trees.
– Deusovi
Dec 16 '16 at 13:37
• @Techidiot your color nodes are rather arbitrary, you only colored some of the intersections, why those in particular? Why not the rest of them? Dec 16 '16 at 14:07
• Most obvious feature (something that seems "forced", with little scope for actual information to be encoded in it) of how the maze looks is the "spurs" of length 1,3,5,7 (maybe also the length-3 spur before the 1, but that's not quite so consistent between bottom left and top right) on each side. Dec 16 '16 at 14:15
• Plus the near rotational symmetry, of course. Dec 16 '16 at 14:17