Counting the number of corners was a very useful hint for part 2. I had the most trouble with detecting the double corners, i.e. like in the example where the two B fields touch diagonally:

AAAAAA
AAABBA
AAABBA
ABBAAA
ABBAAA
AAAAAA

Still, I would’ve taken a lot longer and probably made really-bad-performance-code without reading this :D

Nice :D
How’s the speed now?

Welp, got frustrated again with part one because there kept being something wrong with my totally-not-ugly loop and so came here again. I did have to change IsInt (and thus also Cost to account for different handling) for part two though because I kept getting wrong results for my input.
I’m guessing it’s because uiua didn’t see the difference between rounded and non-rounded number anymore.

Here’s the updated, slightly messier version of the two functions that worked out for me in the end :D

IsInt ← ≍°⊟⍉⍜(⊙(⍉≡↙₂))(/+×)⊙⍉⁅
Cost  ← /+×3_1×⟜IsInt⊸AB

_{Could have been done better but I’m lacking the patience for that now}

Uiua

Ok, so part one wasn’t too hard, and since uiua also takes negative values for accessing arrays, I didn’t even have to care about converting my modulus results (though I did later for part two).
I’m a bit conflicted about the way I detected the quadrants the robots are in, or rather the way the creation of the mask-array happens. I basically made a 11x7 field of 0’s, then picked out each quadrant and added 1-4 respectively. Uiua’s group (⊕) function then takes care of putting all the robots in separate arrays for each quadrant. Simple.

For part two, I didn’t even think long before I came here to see other’s approaches. The idea to look for the first occurrence where no robots’ positions overlapped was my starting point for what follows.

$ p=0,4 v=3,-3
$ p=6,3 v=-1,-3
$ p=10,3 v=-1,2
$ p=2,0 v=2,-1
$ p=0,0 v=1,3
$ p=3,0 v=-2,-2
$ p=7,6 v=-1,-3
$ p=3,0 v=-1,-2
$ p=9,3 v=2,3
$ p=7,3 v=-1,2
$ p=2,4 v=2,-3
$ p=9,5 v=-3,-3
.
PartOne ← (
  # &rs ∞ &fo "input-14.txt"
  ⊜(↯2_2⋕regex"-?\\d+")≠@\n.
  ≡(⍜⌵(◿11_7)+°⊟⍜⊡₁×₁₀₀)
  ↯⟜(▽×°⊟)7_11 0
  ⍜↙₃(⍜≡↙₅+₁⍜≡↘₆+₂)
  ⍜↘₄(⍜≡↙₅+₃⍜≡↘₆+₄)
  /×≡◇⧻⊕□-₁⊸(⊡:)⍉
)

PartTwo ← (
  # &rs ∞ &fo "input-14.txt"
  ⊜(↯2_2⋕regex"-?\\d+")≠@\n.
  0 # number of seconds to start at
  0_0
  ⍢(◡(≡(⍜⌵(◿11_7)+°⊟⍜⊡₁×):)◌
    ◿[11_7]≡+[11_7]
    ⊙+₁
  | ≠⊙(⧻◴)⧻.)
  ⊙◌◌
  -₁
)

&p "Day 14:"
&pf "Part 1: "
&p PartOne
&pf "Part 2: "
&p PartTwo

Now on to the more layered approach of how I got my solution.

In my case, there’s two occasions of non-overlapping positions before the christmas tree appears.
I had some fun trying to get those frames and kept messing up with going back and forth between 7x11 vs 103x101 fields, often forgetting to adjust the modulus and other parts, so that was great.

In the end, I uploaded my input to the online uiua pad to make visualizing possible frames easier since uiua is able to output media if the arrays match a defined format.

I used this code to find the occurrence of non-overlapping positions (running this locally):

&rs ∞ &fo "input-14.txt"
⊜(↯2_2⋕regex"-?\\d+")≠@\n.
0 # number of seconds to start at
0_0
⍢(◡(≡(⍜⌵(◿101_103)+°⊟⍜⊡₁×):)◌
  ◿[101_103]≡+[101_103]
  ⊙+₁
| ≠⊙(⧻◴)⧻.)
⊙◌◌
-₁

Whenever a new case was found, I put the result into the code in the online pad to check the generated image, and finally got this at the third try:

Damn that’s a lot time saved. I love how unassuming the addition looks for how great an effect it has

Uiua

Put this one off for a bit and I’ll put off part two for even longer because I don’t want to deal with any pyramid-shapes of boxes at the moment.
The code for part one feels too long but it works and runs <2s so I’m happy with it for now ^^

Run with example input here

$ ##########
$ #..O..O.O#
$ #......O.#
$ #.OO..O.O#
$ #..O@..O.#
$ #O#..O...#
$ #O..O..O.#
$ #.OO.O.OO#
$ #....O...#
$ ##########
$ 
$ <vv>^<v^>v>^vv^v>v<>v^v<v<^vv<<<^><
$ <><>>v<vvv<>^v^>^<<<><<v<<<v^vv^v>^
$ vvv<<^>^v^^><<>>><>^<<><^vv^^<>vvv<
$ >><^^v>^>vv<>v<<<<v<^v>^<^^>>>^<v<v
$ ><>vv>v^v^<>><>>>><^^>vv>v<^^^>>v^v
$ ^<^^>v^^>v^<^v>v<>>v^v^<v>v^^<^^vv<
$ <<v<^>>^^^^>>>v^<>vvv^><v<<<>^^^vv^
$ <vvv>^>v<^^^^v<>^>vvvv><>>v^<<^^^^^
$ ^><^><>>><>^^<<^^v>>><^<v>^<vv>>v>>
$ >^v><>^v><<<<v>>v<v<v>vvv>^<><<>^><
$ ^>><>^v<><^vvv<^^<><v<<<<<><^v<<<><
$ <<^^<v<^^^><^>>^<v^><<<^>>^v<v^v<v^
$ >^>>^v>vv>^<<^v<>><<><<v<<v><>v<^vv
$ <<<>^^v^>^^>>><<^v>>v^v><^^>>^<>vv^
$ <><^^>^^^<><vvvvv^v<v<<>^v<v>v<<^><
$ <><<><<<^^<<<^<<>><<><^^^>^^<>^>v<>
$ ^^>vv<^v^v<vv>^<><v<^v>^^^>>>^^vvv^
$ >vvv<>>>^<^>>>>>^<<^v>^vvv<>^<><<v>
$ v^^>>><<^^<>>^v^<v^vv<>v^<<>^<^v^v>
$ <^<<<><<^<v><v<>vv>>v><v^<vv<>v^<<^

Pos ← :°⊟♭⊚⊸⌕@@
Move ← (
  ⊸⊗@.
  ⍣(+₁⍤.◡(≠⊙⧻)
    ⍜↙⍣(⬚@.↻₋₁⍤.=⊃(⧻|⊗@#).)∘
  )⋅∘
)

PartOne ← (
  # &rs ∞ &fo "input-15.txt"
  ⊜□¬⦷"\n\n".
  ∩°□°⊟
  : ⊙(▽≠@\n.) ⊜∘≠@\n.
  ↘₄⊛⊂"^>v<"
  ⍢(⊃↘₁⊢
    ⊙(⟜(⨬(⍉|∘)◿₂)
      ⟜(⨬(⍜(↘⊙⊡)Move Pos
        | ⍜(⇌↙⊙⊡)Move +₁Pos
        )=₀◿₃)
      ⨬(⍉|∘)◿₂
    )
  | ≠0⧻)
  ◌
  /+≡/+×[100_1]⊚⌕@O
)

PartTwo ← (
  ""
)

&p "Day 15:"
&pf "Part 1: "
&p PartOne
&pf "Part 2: "
&p PartTwo