Generate ASCII TetraVex
Ruby 196
This is an anonymous function that takes width and length as arguments and writes to stdout.
->m,n{r=rand(9)
t=""
128.times{|h|t<<"%02X"%((h+r)*17%256)}
(m*n*4-m).times{|k|i=k%m;j=k/m
s="\\ #{t[j/4]} / | #{t[i]} X #{t[i+1]} | / #{t[j/4+1]} \\ | ------+-"[j%4*8,8]
i==m-1&&s[5,3]=$/
$><<s}}
Explanation
Uniqueness of cells is guaranteed by having the contents of each cell correspond to its x,y coordinates, as below. As a result the pattern is always symmetrical about the NW-SE diagonal:
00,00 01,00 02,00 03,00 04,00 05,00 06,00 07,00 08,00 09,00 10,00 11,00...
00,01 01,01 02,01 03,01 04,01 05,01 06,01 07,01 08,01 09,01 10,00 11,01...
00,00 01,02 02,02 03,02 04,02 05,02 06,02 07,02 08,02 09,02 10,02 11,02...
.
etc
The x values appear on the left and right edges of the tile, and the y values on the top and bottom edges.
The astute will have noticed that we cannot simply write a 2-digit number across each tile, because the edges will not match. What is needed is a sequence of (at least) 255 digits where all combinations are unique. From this we can pick a pair of digits (e.g. 1 and 2) for the first tile , then follow naturally on to the next, where the last number of one tile becomes the first of the next (e.g. 2 and 3).
I use a sequence containing just the hexadecimal digits 0-9A-F because the hexadecimal number representation is more golfable than some other arbitrary base. Therefore I need a 256 digit sequence where every one of the possible 2-digit combinations appears exactly once. Such a sequence is known as a De Bruijn sequence.
I have discovered a very golfy way of generating De Bruijn sequences of subsequence length 2 with digits from even base numbers. We simply take all the numbers from 0 to b*b/2-1, multiply them by b+1,take the last 2 digits, and concatenate the results. Here is an illustration of the sequence used with a bit more explanation as to how it works for base b=16. Basically each line contains all combinations with two of the possible differences between digits, which together add up to 1 or 17 (mod 16). It is necessary to think in modular base 16 arithmetic, where for example -1 = +F.
00112233445566778899AABBCCDDEEFF Difference between digits is +1 or +0
102132435465768798A9BACBDCEDFE0F Difference between digits is +2 or +F
2031425364758697A8B9CADBECFD0E1F Difference between digits is +3 or +E
30415263748596A7B8C9DAEBFC0D1E2F . . . . .
405162738495A6B7C8D9EAFB0C1D2E3F . . . . .
5061728394A5B6C7D8E9FA0B1C2D3E4F . . . . .
60718293A4B5C6D7E8F90A1B2C3D4E5F Difference between digits is +7 or +A
708192A3B4C5D6E7F8091A2B3C4D5E6F Difference between digits is +8 or +9
Finally, to comply with the random requirement, the pattern can be shifted diagonally by a random number 0..8 so there are 9 possible boards that can be generated.
ungolfed in test program
f=->m,n{ #width,height
r=rand(9) #pick a random number
t="" #setup empty string and build a DeBruijn sequence
128.times{|h|t<<"%02X"%((h+r)*17%256)} #with all 2-digit combinations of 0-9A-F
(m*n*4-m).times{|k| #loop enough for rows*columns, 4 rows per tile, omitting last row.
i=k%m;j=k/m #i and j are the x and y coordinates
#lookup the 4 values for the current tile and select the appropriate 8-character segment
# from the 32-character string produced, according to the row of the tile we are on.
s="\\ #{t[j/4]} / | #{t[i]} X #{t[i+1]} | / #{t[j/4+1]} \\ | ------+-"[j%4*8,8]
i==m-1&&s[5,3]=$/ #if i is on the rightmost row, delete the last 3 charaters of s and replace with \n
$><<s}} #print the current horizontal segment of the current tile.
f[20,20]
Output for 20,20 where r=8
\ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \ | / 8 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 / | \ 8 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \ | / 9 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 / | \ 9 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \ | / A \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A / | \ A /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \ | / B \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B / | \ B /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \ | / C \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C / | \ C /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \ | / D \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D / | \ D /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \ | / E \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E / | \ E /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \ | / F \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F / | \ F /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \ | / 0 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 / | \ 0 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \ | / 2 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 / | \ 2 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \ | / 1 \
------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+------
\ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 / | \ 1 /
8 X 8 | 8 X 9 | 9 X 9 | 9 X A | A X A | A X B | B X B | B X C | C X C | C X D | D X D | D X E | E X E | E X F | F X F | F X 1 | 1 X 0 | 0 X 2 | 2 X 1 | 1 X 3
/ 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \ | / 3 \
CJam, 116
26mr:D;q~:B;){[7B),f#10222@#f*2G#)f%_2ew:+23f%\W<26f%]{D+26%'A+}f%~"\/"f*_:$@2/'Xf*[@]'|f*Sf*~_'{f>"-+"f=\@}%2>-3<N*
Try it online
Uses only letters.
Explanation:
The first observation is that any rectangular piece of a solved board is a solved board. Since the program needs to work up to 255×255, it is enough to solve it for that case and use a piece of that board with the requested dimensions.
I am using a fixed 255×255 board that I determined to be correct. I actually did 256×256 tiles first, choosing 2 numbers per tile (top and left), then copied the other numbers from adjacent tiles, discarding some edge numbers from the last row and last column.
Each tile is first given an associated number, and then I calculate the remainders of that number modulo two other numbers (I used 23 and 26) to get the 2 numbers chosen for that tile.
In order to avoid patterns which lead to duplication, I decided to make the associated numbers pseudo-random and unique. I used my favorite distinct not-very-random number generator, which is based on primitive roots: take a prime number slightly bigger than the desired range (65537) and a small prime number (7), then use the powers of the small number modulo the big number. After a few trials, I found that the combination of 7, 23 and 26 works well, giving 65025 (255²) unique tiles.
For the random factor, I am just applying a random cyclic permutation to the value of each number. Then the numbers (0-25) are converted to letters (A-Z).
Code explanation to follow.
APL (Dyalog Unicode), 112 bytes
⎕CY'dfns'
{⍉¯2↓2↓⍉¯1↓1↓(1,⍨3 7×⍳¨⍵)box⊃⍪/,/⍵↑∘.{(7⍴0 1)\3 3⍴⍺@2 8⊢⍵@4 6,⍨'\//\X'}⍨2,/⎕A[(?5)+16|+\17|⊢∘-\32/⍳8]}
Try it online!
An inline function that takes a single argument, a length-2 vector n m.
The essential idea is taken from Level River St's Ruby solution, i.e. build a De Bruijn sequence of order 2 on a size-16 alphabet.
The rest of the algorithm is just extracting alphabets (with random offset to the alphabet index), arranging into boxes, taking the top left corner of size of the input, and formatting to match the output format.
A bit of work is offloaded to the dfns.box library function, which inserts horizontal and vertical dividers at given indexes using either box-drawing Unicode chars or ASCII.
How it works
⍝ Load library to use the function `box`
⎕CY'dfns'
f←{
⍝ Generate the De Bruijn sequence using the observation by Level River St
idxs←16|+\17|⊢∘-\32/⍳8
32/⍳8 ⍝ 1..8, each number copied 32 times
⊢∘-\ ⍝ Negate the even indexes (1-based)
17| ⍝ Modulo 17; gives 1 16 1 16 ... 2 15 2 15 ... 8 9 8 9
16|+\ ⍝ Cumul.sum mod 16
⍝ Generate tile fragments in one dimension
axis←2,/⎕A[idxs+?5]
idxs+?5 ⍝ Add one of 1..5 (random) to all of idxs
⎕A[ ] ⍝ Index into the vector of uppercase letters
2,/ ⍝ Join adjacent pairs
⍝ Generate the matrix of tiles
mat←⍵↑∘.{(7⍴0 1)\3 3⍴⍺@2 8⊢⍵@4 6,⍨'\//\X'}⍨axis
∘.{ }⍨axis ⍝ Self outer product over axis
,⍨'\//\X' ⍝ '\//\X\//\X'
3 3⍴ ⍝ Reshape to 3×3 so the ^ chars form X-frame
⍺@2 8⊢⍵@4 6 ⍝ Place chars of ⍺ vertically, ⍵ horizontally
(7⍴0 1)\ ⍝ Insert blanks between columns and outside
⍵↑ ⍝ Take n rows and m columns of the entire matrix
⍝ Output formatting
⍉¯2↓2↓⍉¯1↓1↓(1,⍨3 7×⍳¨⍵)box⊃⍪/,/mat
⊃⍪/,/mat ⍝ Flatten chars to single matrix
( )box ⍝ Apply box drawing with the options of
3 7×⍳¨⍵ ⍝ inserting lines after every 3rd row and 7th col
1,⍨ ⍝ using ASCII
⍉¯2↓2↓⍉¯1↓1↓ ⍝ Fix formatting: drop 1 rows and 2 columns from the outside
}