text:
Square and square
Squares looks symmetric, and so are the required codes.
Objective: Write a program whose source code is a solid square (N lines with N printable, non-whitespace characters each line) and prints a square of equal size. A program (or output) with inconsistent width and height is invalid. (e.g. 6x5)
Example (HQ9+)
QAA
AAA
AAA

Requirements

Both the source and the output must contain N lines, and N printable characters each line, followed by 1 linefeed. Your program should not contain or output any control characters (except LF or CR-LF) or whitespaces (Space, Tab, VTab)
Standard loopholes are boring, don't use them.
A program (and output) with only one character is fundamentally nothing. N must be at least two.
The content of the output doesn't matter, as long as it complies with rule 1
Special rule: Do not use comments or codes that does not affect the output to "fill" your code.
To be clear, you are allowed to use i++;i++;... i++; instead of i+=10;, but you shouldn't define a variable string s="placeholder" but never use it later. It is very easy to work around this rule so don't be too strict.
If you want to output a newline before everything else, it OK but please declare that you're using this rule.
If you want to output the last line without a succeeding linefeed, it's OK, too and you don't need to declare it. However that does not affect scoring.

Additional: Please give the number N (width/height) your program is using. Provide descriptions of your code if possible.
There is no need to give the length (in bytes) of your program because the N says it all.
Because this is a code-bowling, the program with the largest N and the highest complexity will win.

What's the type of this challenge (e.g. code golf, popularity contest)?

@Jakob Is a popularity contest still allowed?

I'd suggest adding the [tag:restricted-source] tag.

@iBug pop-contests are allowed but they rarely get well-received... :D

I don't think this is up to our standards of popularity contests.  Simply slapping the tag on a question is not sufficient.  Please read the tag wiki for a more detailed guide.

You should also define what is meant by a comment.  This is not a defined term on its own.

Rule of thumb: if a program whose text is 1 and which outputs 1 is a valid answer then the question is badly flawed. Putting in a special rule to disallow that program isn't a proper fix.

@PeterTaylor "N must be at least two.", 1 is a 1 by 1 square meaning it is too small.

@iBug. Can we output a new line before the square?

We've had similar challenges before. I'd suggest making this code-golf, maybe adding restricted-source or quine tags, and maybe dropping the no comments requirement as it's somewhat unclear. Wouldn't see any reasons to not reopen then.

@WheatWizard well that's the special rule isn't it

You might look into [tag:code-bowling]

code-golf doesn't make sense, since every valid entry will have N*(N+1) characters, and I don't think you mean for smaller programs to be "better" than larger programs.

Can the source code be a rectangle like in the N = 6 JavaScript answer or must it be square?

Does the last output line need to end in a linefeed?

There is no actual winning criterion stated in your question.

@Okx Oops! Someone edited it out!

@iBug this had the code-golf tag for a good 7 hours before being changed to the exact opposite - code-bowl. Most answers are trying to find the minimal square that outputs a square. Also, with the given limitations, it is very easy to create arbitrarily large squares in most languages. Adding limitations would once again be unfair to current answers.

Example of arbitrarily large Ruby squares.

Bonus: make it a quine ;)

@iBug is complexity actually a factor in scoring? Also what should be done if arbitrarily large programs can be made?

Seems it's better a code-golf and it's really treated as a code-golf somehow

Voting to close. The question should be changed to [code-golf] because otherwise the weak source restriction makes it too easy, and code can be bowled arbitrarily large.

JavaScript (ES6), N = 5
With a leading newline instead of a trailing newline.

alert
((a=`
`+!!0
)+a+a
+a+a)

JavaScript (ES6), N = 6

alert(
(1e5+`
`)['r'
+'epe\
'+'at\
'](6))

JavaScript, N = 7

this['\
consol\
e'].log
('1234\
567\n'[
'repea\
t'](7))

JavaScript, N = 202

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+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+
[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]]](!+[]+!+[]+!+[]+[+!+[]])[+!+[]]+(!![]+[])[!+[]+!+[]+!+[]])()([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]
]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]][([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[
]]]+[])[!+[]+!+[]+!+[]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+([][[]]+[])[+!+[]]+(![]+[])[!+[]+!
+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[+!+[]]+([][[]]+[])[+[]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]
]+(!![]+[])[+[]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+!+[]]]((!![]+[])[+!+[]]+(!![]+
[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+([][[]]+[])[+[]]+(!![]+[])[+!+[]]+([][[]]+[])[+!+[]]+(+[![]]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+
(!![]+[])[+!+[]]])[+!+[]+[+!+[]]]+(!![]+[])[!+[]+!+[]+!+[]]+(![]+[])[!+[]+!+[]+!+[]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[
+!+[]]]+[])[!+[]+!+[]+!+[]]+(![]+[])[+!+[]]+(+(!+[]+!+[]+[+!+[]]+[+!+[]]))[(!![]+[])[+[]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+
(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(+![]+([]+[])[([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[][(!
[]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+([][[]]+[])[+!+[]]+(![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[
+!+[]]+([][[]]+[])[+[]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[][(![]+[])[
+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+[]]+(!![]+[])[+!+[]]+([![]]+[][[]
])[+!+[]+[+[]]]+([][[]]+[])[+!+[]]+(+![]+[![]]+([]+[])[([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!
![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+([][[]]+[])[+!+[]]+(![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(
!![]+[])[+!+[]]+([][[]]+[])[+[]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[][
(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]]](!+[]+!+[]+!+[]+[+!+[]])[+!+[]]
+(!![]+[])[!+[]+!+[]+!+[]])()(([]+[])[([![]]+[][[]])[+!+[]+[+[]]]+(!![]+[])[+[]]+(![]+[])[+!+[]]+(![]+[])[!+[]+!+[]]+([![]]+[][[]])[+!+[]+[+[]]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+
[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(![]+[])[!+[]+!+[]+!+[]]]()[+[]])[+[]]+(!+[]+!+[]+[!+[]+!+[]+!+[]+!+[]+!+[]+!+[]+!+[]])+[])+(!![]+[][(![]+[])[+[]]
+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]]+(+(+!+[]+[+!+[]]+(!![]+[])[!+[]+!+[]+!+[]]+[!+[]+!+[]]+[+[]])+[])[+!+[]]+(!!
[]+[])[+!+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(+(!+[]+!+[]+[+!+[]]+[+!+[]]))[(!![]+[])[+[]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![
]+[])[+!+[]]])[+!+[]+[+[]]]+(+![]+([]+[])[([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[][(![]+[
])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+([][[]]+[])[+!+[]]+(![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[+!+[
]]+([][[]]+[])[+[]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[][(![]+[])[+[]]
+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+[]]+(!![]+[])[+!+[]]+([![]]+[][[]])[+
!+[]+[+[]]]+([][[]]+[])[+!+[]]+(+![]+[![]]+([]+[])[([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+
[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+([][[]]+[])[+!+[]]+(![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]
+[])[+!+[]]+([][[]]+[])[+[]]+([][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[][(![]
+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[+!+[]+[+[]]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]]](!+[]+!+[]+!+[]+[+!+[]])[+!+[]]+(!!
[]+[])[!+[]+!+[]+!+[]]+(![]+[])[+!+[]]+(!![]+[])[+[]]+(![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]]+[
!+[]+!+[]]+[+[]]+[+[]]+(+(+!+[]+(!+[]+[])[!+[]+!+[]+!+[]]+[+!+[]]+[+[]]+[+[]])+[])[!+[]+!+[]]+[!+[]+!+[]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[
!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]]+(!![]+[][(![]+[])[+[]]+([![]]+[][[]])[+!+[]+[+[]]]+(![]+[])[!+[]+!+[]]+(!![]+[])[+[]]+(!![]+[])[!+[]+!+[]+!+[]]+(!![]+[])[+!+[]]])[!+[]+!+[]+[+[]]])()

Here is for N = 4 (I'm just not sure if the new line on the beginning is allowed).

I have a solution for N=5 https://pastebin.com/9NFjBbxT

Here's a solution for N=4 without a leading newline in the output https://pastebin.com/pGvBQ1VK

That N=6 solution is invalid because there's only 5 lines.

I believe what I've said is a square, not a rectangle.

@iBug Whoops, fixed that!

@kamoroso94 I'm not sure functions are allowed, the challenge requires a program.

Perl 5, 5×5
print
q.u.x
$],$/
for(t
..x);

This is very slightly obfuscated to make it more interesting, so here's some explanation: q.u. is just the same as 'u'. The following x is the repetition operator, so 'u' is repeated $] times. $] is between 5 and 6, so 'u' gets repeated 5 times. You then append the newline $/ and print the whole thing. This is all done once for each member of the list t..x: t and x as barewords are assigned the values 't' and 'x' respectively, and the list is thus 't','u','v','w','x'. So the output is:
uuuuu
uuuuu
uuuuu
uuuuu
uuuuu

Your complete explanation deserves an upvote.

Ruby, 3x3
!p\
p,\
p,p

Prints
nil
nil
nil

Try it online!
How it works
p is a method that prints each of its arguments, then returns the value (or an array of the values) that it printed. If it's called without an argument, it doesn't print anything and returns nil. Thus the ps on lines 2 and 3 all evaluate to nil, and the first p prints those nils.

C, N=7
i;main(
){for(i
=01;i<=
56;i++)
putchar
(i%8?37
:012);}

Prints a 7x7 grid of %, i.e.
%%%%%%%
%%%%%%%
%%%%%%%
%%%%%%%
%%%%%%%
%%%%%%%
%%%%%%%

Charcoal, n=2
Boring solution (Charcoal just prints ASCII literally):
sq
re

Try it online!

Would this mean you could make the program arbitrarily large, because it would just print itself?

Yeah (random filler text to make this comment over 15 characters)

Same can be said for php if the file doesn't start with <? / <?php.

Python 3, 29 bytes
eval(
'pri\
nt(1\
/8),'
*-~4)

Try it online!
5x5 can be done. Prints:
0.125
0.125
0.125
0.125
0.125

brainfuck, 9x9
++[->+++<
]>+++[->+
>+<<]<--[
>+<++++++
]><<++[->
+++++<]>>
>>[<[-<.>
]<<.>>+++
++++++>-]

Try it online!
Outputs  a square of + (the most fundamental function of brainfuck).
I'll be back when I figure out how to convert this into a quine, so rougly 3 weeks or so...

Still have not figured out how to quine this.

Nothing has changed

Haskell, 7x7 6x6
f=b>>y
y=b++n
n="\n"
b=c++d
c=d++d
d="--"

Outputs
------
------
------
------
------
------

Try it online!
How it works:
f=             -- main function which returns the string
  b>>y         --   length b copies of y, i.e. 6 times y, because:

d="--"         -- basic building block of the string
c=d++d         -- c -> "----"
b=c++d         -- b -> "------" -> b has length 6
y=b++n         -- y -> 6 dashes plus newline "-------\n"

With compiler flags allowed there's a 5x5 solution:
Haskell, 5x5 (with -cpp compiler flag)
(>>)\
[1,2\
..5]\
"abc\
de\n"

Try it online!
-cpp invokes the cpp preprocessor which enables line folding via \.

What happened to the 7x7? It seems fine, but I'm not familiar with Haskell.

@SolomonUcko:  Although the OP says that the largest square wins, everybody tried to get as small as possible, because it's trivial to make huge squares by filling in unnecessary stuff (even within the rules of the challenge). After my 7x7 I found a 6x6 solution so I updated my answer.

Ok, that makes sense. I guess you could post both?

@SolomonUcko: sure, but the 7x7 is basically the same as the 6x6, so it's not very interesting.

True. It looks like the change is mostly just changing variable names, removing semicolons, and removing an unnecessary assignment statement.

SOGL V0.12, N = 3 2
H$
$Q

Try it Here!
The first line - H$ means in the continuing lines replace $ with H, resulting in the next line being HQ. That then gets executed:
H   decrease POP (nothing on the stack so input (no input so 0)) - results in 0-1 = -1
 Q  output that without popping
    implicitly output POP as none of `tTpP` were called

Found this by brute forcing trough all programs on length 2 (as any program like ..\n.. will always come down to a 2 character program)

Python 2, n=6
print\
'\n'.\
join(\
['###\
###']\
*+~-7)

Try it online!
Not as golfed as it could be, but... I have to fill up the gaps somehow don't I :P

I don't think this can further be golfed... because print itself is 6 bytes and 1 byte '' is the lowest compulsion.

Yeah, I meant as in it can be golfed to ~16 bytes if there were no source format restrictions

@officialaimm well technically you could build the string "print" and then eval it, but I think you'll go too far down to fit into a 5x5...

@StepHen oh yeah... eval might be a remedy...

Ruby, n=6 5
Saved 12 bytes thanks to m-chrzan
puts(
"Rub\
y!\n\
"*(1+
2+2))

Try it online!
Yes, I'm intending to Leaky Nun this EDIT: :/ source restrictions are worse than I thought for most esolangs, and normal languages as well

5x5 with puts.

><>, N = 3
"vn
:/^
ao/

It prints
110
110
118

Try it online, or watch it at the fish playground!
This is a little tricky, so bear with me. The fish starts in the top left corner, and immediately enters string mode. It pushes the charcodes of "v" and "n" to the stack, which are 118 and 110 respectively. The fish then wraps and hits the " again, exiting string mode. The v then sends the fish downward, and the / reflects it left into :, which duplicates the top of the stack: the stack is now 118, 110, 110.
The fish then wraps and ^ sends it into a loop:
  n
  ^
ao/

This loop prints the top of the stack as a number (n), wraps and bounces, pushes a = 10 = linefeed to the stack, then prints it as a character (o) and starts the loop again. When the stack is empty, n causes an error and the program halts.

It's been pointed out in the comments that halting with an error is rather unsatisfying. I therefore give you an alternative that halts naturally, in a 4x4 square:
aa|v
no"/
lo~/
;!?/

It prints
/110
/110
/110
/110

Try it online!

Does printing something smells fishy... not count, since technically that's printed when the program errors (IIRC it's printed to STDOUT).

@cole, I'm pretty sure it prints to STDERR, which is ignored by default. Stopping with an error is a very common way of halting ><> programs. If you really want error-free code, though, I can fit it in a 5x5 square: Try it online!

I must be forgetting my ><>. I like both solutions, by the way (and I think the 3x3 is especially clever).

V, 11 bytes
3éi
3Äh
hhh

Try it online!
éi
.Ä

Should be a valid 5 byte solution, but unfortunately that functionality is missing. :(

Hey, the N is inconsistent!

Does this work?  It works in Vim but I don't know V

CJam, n=∞
Root version: n=2
AN
BN

Try it Online
Prints
10
11

Can be extended to any n by prepending numbers to each line. E.g:
n=11
123456789AN
123456789AN
123456789AN
123456789AN
123456789AN
123456789AN
123456789AN
123456789AN
123456789AN
123456789AN
Prints
12345678910
12345678910
12345678910
12345678910
12345678910
12345678910
12345678910
12345678910
12345678910
12345678910
12345678910
Try it Online

Python 3, N = 13 (181 bytes)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)
print("#"*13)

Try it online!
I don't see why this wouldn't be valid, since there is no rule that enforces me to not use this technique (I think). This prints a 13x13 grid of octothorpes.

Aceto, 3x3
Cast the implicit zero to a float (0.0), duplicate, print, newline, duplicate, print, newline, print, newline.
dpn
npp
fdn

Old version that may be invalid:
Aceto is sort of made for this sort of challenge; all programs are squares, at least internally. It may or may not be valid, as in the output the final line does not end with a linefeed. We simply calculate 2^7, turn on sticky mode, and print three times with newlines inbetween.
pnp
kFn
27p

Gaia, 3 x 3
3/ṣ
ṙ×↑
9:⇈

Try it online!
Explanation
9    Push 9
 :   Copy it
  ⇈  Call the function above
ṙ    String representation of 9
 ×   Repeated 9 times
  ↑  Call the function above
3/   Split into chunks of 3
  ṣ  Join with newlines

Gaia, 2 x 2
gp
Ø↑

I'm not sure if this is valid since it's a cheating quine (Øg reads the program's source file).

PHP, n=∞
I don't know if this is a loophole, but here is the 2 version :
aa
aa

Prints
aa
aa

Try it online!
With n=10
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa

Try it online!
Can be extended to any number.

(I don't think it's a loophole, I think it's an example of why we don't do code-bowling).

Python 3, n=6
print\
('\n'\
.join\
(['$$\
$$$$'\
]*+6))

Try it online!
Almost the same as the Python 2 answer, just with parens :/
I can make it more different if anyone wants :P

Proton, N = 5
print
(5*("
$$$$$
"[1to
7]));

Try it online!

Ly, 11 bytes
"r(
34)
r&o

Try it online!
A standard quine put in the shape of a square.

Perl 5, 4x4
(say
1111
)for
1..4

Try it online!
Requires -M5.010 on the command line.

BTW, does cmdlinearg -M5.010 have the same effect as a line in file that reads use 5.010;?

@iBug usually use 5.010 or -M5.010 can be deemed as free, since most of the features imported by it can be accessed by running the script via perl -E instead of perl -e which is the same length.

Don't think there's a length 3 var (not that I can see in perlvar anyway) otherwise you could get a 3x3 with something like this... Will play with this today though!

brainfuck, N=6
++++++
++++>-
--->++
++++[<
......
<.>>-]

Arguably this isn't valid as I arbitrarily chose the output char to be 3 codepoints lower to fix the sqaure...
Try it online!

TI-BASIC, N = 2
Disp Xmax
Disp Xmax

Note that Disp  (including the space) and Xmax are each one character. Since Xmax is 10 by default, the output is:
10
10

WendyScript, 5x5
for i
:0->5
{#j :
0->5@
i ""}

produces:
00000
11111
22222
33333
44444

Try it online!

Python 2, n=5
exec(
'pri\
nt "\
5"*5\
;'*5)

Try it online!
Python 2 variant of Sisyphus' answer

Excel VBA, n = 15
Declared subroutine that takes in an empty input variable, (for output) and outputs to range [A1], via a messagebox and to VBE immediate window, and via the input variable
Sub$A(n):s="1|"
s=s+"2"+"|"+"3"
s=s+"|"+"4"+"|"
s=s+"5"+"|"+"6"
s=s+"7|8|9|0|1"
s=s+"2|3|4"+"|"
s=s+Chr(51+9-7)
tu=Split(s,"|")
var=Join(tu,"")
[B1]=var+vbCrLf
o=[Rept(B1,15)]
MsgBox$o,0,"hi"
Let[A1]=CStr(o)
Debug.Print[A1]
n=o:End:End$Sub

The above autoformats to
Sub A(n): s = "1|"
s = s + "2" + "|" + "3"
s = s + "|" + "4" + "|"
s = s + "5" + "|" + "6"
s = s + "7|8|9|0|1"
s = s + "2|3|4" + "|"
s = s + Chr(51 + 9 - 7)
tu = Split(s, "|")
Var = Join(tu, "")
[B1] = Var + vbCrLf
o = [Rept(B1,15)]
MsgBox$ o, 0, "hi"
Let [A1] = CStr(o)
Debug.Print [A1]
n = o: End: End Sub

and outputs
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345
123456789012345

Runic Enchantments, n=∞ (min 7x7)
"'.<~SD|
"'.<~SD|
"'.<~SD|
"'.<~SD|
"'.<~SD|
"'.<~SD|
"'.<~SD|
k@."0<Ra

Try it online!
Heavily leverages Runic's ability to handle multiple instruction pointers simultaneously. What's one quine doubled? Why, one quine twice as long.
All the . commands are how the basic quine expression "'<~S@| can be expanded to be of arbitrary width. Additional copies of the quine expand the square vertically. Newlines and output are handled by the last line, funneling all of the quine IPs to a single terminator expression, following Rak@, which pushes a newline character, then dumps the entire stack top to bottom to output. The last line itself also produces a line of output, .@kaR<00, in order to maintain the requisite structure size. As the last line outputs first, there is no leading or trailing newline.
There are shorter quines (namely '<~@|"), however the last line is hard-limited to 7 characters, or it cannot produce output of the correct width (@"<Rak is 6 characters long, but outputs only 5 characters).
I also attempted to code the smallest possible square. This was the best I could do.
Runic Enchantments, n=6
\>1CYS
\:$1Xk
\:$S:$
\S:$S:
\$S:$S
\:$q:@

Try it online!
Repeatedly clones the top of the stack, prints it, and swaps the top two items in order to print 100000 six times with 5 interwoven newlines.
And then, because I could:
Runic Enchantments, n=9
\>311+6Xk
\w421+akw
\"'{~Sak"
\"@|."'"S
\q:1K1K1K
\1K1K1K1K
\1K1K1KE:
\E:E:E:1K
\311++*E;

Try it online!
9x9 square program that outputs a 9x9 square quine (with leading newline).
This is accomplished by creating the 9-byte quine as a string and then Eval'ing it 4 times, then multiplying the string by 5 ("abc"*3 -> "abcabcabc") and Evaling one more time for the last 5 copies. This is done this way in order to fill the 9x9 square right to the brim.

Wolfram Language (Mathematica), n = 5
Do[1+
Echo[
+100*
+100]
,5*1]

Outputs
>> 10000
>> 10000
>> 10000
>> 10000
>> 10000

Assume that you does not count >> that would be shortest because only printing function is Print and Echo. Also you have to put at least 1 character after the function to call it.
Map[1+
Print@
#+10&,
Array[
9^6+1+
#&,6]]

Try it online!
Outputs
531443
531444
531445
531446
531447
531448

with a trailing newline
n = 7
Print/@
Array[0
+0+0+0+
0+0+0+0
+0+0+0+
1234557
+10&,7]

Try it online!
Outputs
1234567
1234567
1234567
1234567
1234567
1234567
1234567

with a trailing newline

Perl 5, 9x9
for(1..$=
/7){$qq=(
$q=$_)**7
;for($qq%
7..$q/7){
map{print
qq,qqq,,,
qq,qqqqqq
,,}0..2}}

Explanation
The outer for loop is over the sequence 1 .. ($= / 7). $= is 60, so the loop runs from 1 to the floor of 60/7, which is 8.
The first statement in the outer loop, $qq = ($q=$_)**7, assigns the variable $q the value of the index $_ of the loop, and assigns $qq the value $q to the seventh power.
Then comes the inner loop, which is over the sequence $qq % 7 .. $q / 7 (% is modulo).
For this value of $q,      the inner loop is over this sequence:
          1                             1 .. 0
          2                             2 .. 0
          3                             3 .. 0
          4                             4 .. 0
          5                             5 .. 0
          6                             6 .. 0
          7                             0 .. 1
          8                             1 .. 1

Thus the inner loop runs three times in total: twice when the outer loop index is 7, and once when the outer loop index is 8.
The inner loop does map{...} 0..2 which is another loop, this time over the sequence 0 .. 2, so it does the following three times:
print
qq,qqq,,,
qq,qqqqqq
,,

The qqs are the double-quote operator, so this just prints qqq and qqqqqq<newline>.
Thus, the output is
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq
qqqqqqqqq

Try it online.

05AB1E, code-bowling N=∞ (\$\geq7\$), ∞ (\$\geq55\$) bytes
"AAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
"¬ì¬7×«

Try it online or try it with a larger example or verify that the output is a square.
Explanation:
The amount of A on every line can be increased, and an equal amount of additional lines of As are added as well. Also, the A can be any character of your own choice.
"AAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
AAAAAAA
"        # Push this string
 ¬       # Get the first character of this string (without popping)
  ì      # Prepend this character to the string
   ¬     # Get the first character again (without popping)
    7×   # Repeat it 7 times
      «  # And append it to the string (which is output implicitly as result)

05AB1E, code-golf N=2, 5 bytes
0º
∊?

Try it online.
Explanation:
0     # Push 0
 º    # Mirror it horizontally: "00"
  ∊   # Mirror it vertically: "00\n00"
   ?  # Print it without trailing newline

Python 3, N=200, 40199 bytes
print("##################################################"*"#######################################################################################################".count("#########################"))
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print("##################################################"*"#######################################################################################################".count("#########################"))

Try it online!
You can theoretically extend this indefinitely. Based on Mr. Xcoder's method of repeating print statements.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/