Write a square program that outputs the number of times it has been "unrolled"

Question

Consider a square block of text, N characters wide by N tall, for some odd integer N greater than 1.

As an example let N = 5 and the text be:

MLKJI
NWVUH
OXYTG
PQRSF
ABCDE

Notice that this is the alphabet (besides Z) spiraled around counter-clockwise from the lower left corner. It's kind of like a rolled up carpet.

Spiral Alphabet

"Unrolling" the text by one quarter turn clockwise so FGHI are on the same level as ABCDE results in:

 PONM
 QXWL
 RYVK
 STUJ
ABCDEFGHI

This unrolling can be done 7 more times until the text is a single line:

 SRQP
 TYXO
 UVWN
ABCDEFGHIJKLM
 UTS
 VYR
 WXQ
ABCDEFGHIJKLMNOP
 WVU
 XYT
ABCDEFGHIJKLMNOPQRS
 XW
 YV
ABCDEFGHIJKLMNOPQRSTU
 YX
ABCDEFGHIJKLMNOPQRSTUVW
 Y
ABCDEFGHIJKLMNOPQRSTUVWX
ABCDEFGHIJKLMNOPQRSTUVWXY

Challenge

The challenge is to write a program that is an ×ばつN block of text that outputs the number of times it has "unrolled" by a quarter turn when it is rearranged into the unrolling patterns and run.

There are really two contests here: (hopefully it won't be too messy)

1. Do this with the smallest N. (down to a limit of N = 3)
2. Do this with the largest N. (no limit)

There will not be an accepted answer but the winner in each of these categories will receive at least 50 bounty rep from me. In case of ties the oldest answers win.

Example

If your code block is

MyP
rog
ram

running it as is should output 0.

Running

 rM
 oy
ramgP

should output 1.

Running

 or
ramgPyM

should output 2.

Running

 o
ramgPyMr

should output 3.

Finally, running ramgPyMro should output 4.

Details

• The output should be printed to stdout (or the closest alternative) by itself. There is no input.
• You may only use printable ASCII (hex codes 20 to 7E, that includes space) in your code.
• Spaces fill the empty space in the unrolling arrangements. (Unless you're unrolling to the left.)
• Only the arrangements from completely square to completely flat need to have valid output. No other arrangements will be run.
• You may not read your own source.
• You may use comments.
• N = 1 is excluded since in many languages the program 0 would work.

• If desired you may unroll to the left rather than the right. So e.g.

  MyP
  rog
  ram
  

  becomes

  Pg
  yo
  Mrram
  

  and so on. No extra spaces are added when rolling this way. The lines just end

(Related: Write a Rectangular Program that Outputs the Number of Times it was Rotated)

• John Dvorak: Before I read the "challenge" paragraph, I was expecting a challenge to write a program that outputs itself unrolled
• John Dvorak: why does N have to be odd?
• Calvin's Hobbies: @JanDvorak I suppose N didn't have to be odd, but it makes the spirals more standardized. It's staying that way but feel free to post an N = 2 as a comment if you find one.
• Falko: Just an idea: Unrolling the "carpet" to the right creates many lines starting with whitespace, eliminating languages like Python. If you'd allow unrolling to the left, there'd be no need for additional whitespace and Python is (theoretically) possible.
• Justin: Do you have a magic book with infinite great challenge ideas? How else do you keep coming up with such interesting challenges?

Answer 1

Golfscript, N <- [5,7..]

. .
 . . 
 .. 
. .#
],9\-

Fully unrolled:

],9\-# . . . . . ...

Explanation:

• . (multiple times) - duplicate the input
• ] - collect the stack into a single array
• , - take its length
• 9\- - subtract it from 9
• # - line comment

Whitespace is a NOP, but any other NOP would have worked just as well.

Fully rolled up, it uses nine copies of the input (contents ignored) as the stack; 9 - 9 = 0; it has not been unrolled.

Each unroll hides one more dot (duplicate) behind the comment, shrinking the stack once, incrementing the output.

Fully unrolled, it uses only the input (contents ignored) as the stack; 9 - 1 = 8; it has been unrolled 8 times.

The same approach works for any N> 4: Change 9 to the appropriate value of 2*N+1, then extend the pattern of dots (duplicate) using the same spiral pattern that ensures exactly one dot gets unrolled during each unroll.

• Calvin's Hobbies: Well, unless someone finds N = 3, this will be the winning answer in both categories.
• John Dvorak: @Calvin'sHobbies should I be a total dick and post a left-unrolling solution as well? :-)
• Calvin's Hobbies: Why not. Another answer seems unlikely otherwise :P
• Beta Decay: Why not go for one which can unroll in both directions? :)
• John Dvorak: @BetaDecay hmm... :-)

Answer 2

GolfScript, N = 4

This one right rolls as original spec.

.. . 
...# 
.#.~
],8-

Here are the unrolls:

 ...
 #..
 ..
],8-~#.
 .#.
 ...
],8-~#. ..
 ..
 .#
],8-~#. ....
 ..
],8-~#. ....#.
 .
],8-~#. ....#..
],8-~#. ....#...

Try it here

• proud haskeller: How did you think of this arrangement?
• Optimizer: @proudhaskeller It's better if you don't know ...
• proud haskeller: Did you brute-search a solution?
• John Dvorak: Special challenge: can you make one out of .s and #s?
• John Dvorak: I like the trailing ~. Maybe I can steal it for N=3?

Answer 3

APL, N = 3

201
340
5|0

Unrolled:

 32
 40
5|001
 43
5|00102
 4
5|001023
5|0010234

Try it online.

It calculates the remainder of that number divided by 5. Only the result of last line is printed.

APL, N = 2

⍬∞
≡0

Unrolled:

 ⍬
≡0∞
≡0∞⍬

Try it online.

≡ returns the depth (not to be confused with the dimension or length) of an array:

• 0 is not an array. So the depth is 0.
• 0∞ is an array with two items 0 and ∞ (infinity). It has depth 1.
• 0∞⍬ has another item ⍬, which is an empty array with depth 1. So 0∞⍬ has depth 2.

These two programs also works in the online interpreter. I'm not sure if the later one is syntactically correct.

⍬0
≡∞

⍬ ̄
≡0

APL, for any N>= 4

For N = 4:

∞ ∞
 ∞∞
∞ ∞
⍴1↓∞

Fully unrolled:

⍴1↓∞ ∞ ∞ ∞ ∞∞∞

For N = 5:

∞ ∞
 ∞ ∞
 ∞∞
∞ ∞
⍴1↓ ∞

Fully unrolled:

⍴1↓ ∞ ∞ ∞ ∞ ∞ ∞ ∞∞∞

1↓ removes an item in the array. It also returns the empty array if the argument is scalar. ⍴ gets the array length.

• proud haskeller: Any explanations?
• jimmy23013: @proudhaskeller Edited.
• Optimizer: You can ideally use the same depth logic for any N. Thanks to APL
• jimmy23013: @Optimizer It is not that easy. Things before the last line still have to be syntactically correct. So I can't use most of the functions or other punctuation characters like ()[] as they will appear at some unwanted place.
• Optimizer: I meant like: ` ⍬ \n⍬⍬0\n≡ ∞` (Not exactly that, but you get the idea)

Answer 4

Perl 5 + -p0513, 155 bytes, N=12

Not particularly competitive, but it was fun trying to get to this point. I tried with 1s originally, but struggled to make it work with 1s only separated by newlines. Also investigated using just list length (N=6) but had issues without using length and join.

# #
 # #;
 # # w
 # # q
 # # ,
 ## '
 # # '
 # # n
 # # i
 # # o
# #j
$\+=length 

Try it online!

1, 2, 3, ..., 18, 19, 20, 21, 22

Answer 5

Vyxal, N=3

› ›
›› 
0 

Try it Online!

Unrolled:

 ››
 › 
0 ›
 ››
0 › ›
 ›
0 › ››
0 › ›››

› increments a number, so the rolled version prints 0, the once-unrolled version prints 0+1=1, the twice-unrolled version prints 0+1+1=2 and so on. This could probably be extended to arbitrary-sized grids.

• Shaggy: N must be at least 3
• emanresu A: @Shaggy Ah. The APL answer has a solution with n=2. Will fix