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--- Part Two ---
After careful analysis, one thing is certain: [1m[97myou have no idea where all these bugs are coming
from[0m.
Then, you remember: Eris is an old Plutonian settlement! Clearly, the bugs are coming from
recursively-folded space.
This 5x5 grid is [1m[97monly one[0m level in an [1m[97minfinite[0m number of recursion levels. The tile in the middle of
the grid is actually another 5x5 grid, the grid in your scan is contained as the middle tile of a
larger 5x5 grid, and so on. Two levels of grids look like this:
| | | |
| | | |
| | | |
-----+-----+---------+-----+-----
| | | |
| | | |
| | | |
-----+-----+---------+-----+-----
| | | | | | | |
| |-+-+-+-+-| |
| | | | | | | |
| |-+-+-+-+-| |
| | | |?| | | |
| |-+-+-+-+-| |
| | | | | | | |
| |-+-+-+-+-| |
| | | | | | | |
-----+-----+---------+-----+-----
| | | |
| | | |
| | | |
-----+-----+---------+-----+-----
| | | |
| | | |
| | | |
(To save space, some of the tiles are not drawn to scale.) Remember, this is only a small part of
the infinitely recursive grid; there is a 5x5 grid that contains this diagram, and a 5x5 grid that
contains that one, and so on. Also, the ? in the diagram contains another 5x5 grid, which itself
contains another 5x5 grid, and so on.
The scan you took (your puzzle input) shows where the bugs are [1m[97mon a single level[0m of this structure.
The middle tile of your scan is empty to accommodate the recursive grids within it. Initially, no
other levels contain bugs.
Tiles still count as [1m[97madjacent[0m if they are directly [1m[97mup, down, left, or right[0m of a given tile. Some
tiles have adjacent tiles at a recursion level above or below its own level. For example:
| | | |
1 | 2 | 3 | 4 | 5
| | | |
-----+-----+---------+-----+-----
| | | |
6 | 7 | 8 | 9 | 10
| | | |
-----+-----+---------+-----+-----
| |A|B|C|D|E| |
| |-+-+-+-+-| |
| |F|G|H|I|J| |
| |-+-+-+-+-| |
11 | 12 |K|L|?|N|O| 14 | 15
| |-+-+-+-+-| |
| |P|Q|R|S|T| |
| |-+-+-+-+-| |
| |U|V|W|X|Y| |
-----+-----+---------+-----+-----
| | | |
16 | 17 | 18 | 19 | 20
| | | |
-----+-----+---------+-----+-----
| | | |
21 | 22 | 23 | 24 | 25
| | | |
- Tile 19 has four adjacent tiles: 14, 18, 20, and 24.
- Tile G has four adjacent tiles: B, F, H, and L.
- Tile D has four adjacent tiles: 8, C, E, and I.
- Tile E has four adjacent tiles: 8, D, 14, and J.
- Tile 14 has [1m[97meight[0m adjacent tiles: 9, E, J, O, T, Y, 15, and 19.
- Tile N has [1m[97meight[0m adjacent tiles: I, O, S, and five tiles within the sub-grid marked ?.
The rules about bugs living and dying are the same as before.
For example, consider the same initial state as above:
....#
#..#.
#.?##
..#..
#....
The center tile is drawn as ? to indicate the next recursive grid. Call this level 0; the grid
within this one is level 1, and the grid that contains this one is level -1. Then, after
[1m[97mten[0m minutes, the grid at each level would look like this:
Depth -5:
..#..
.#.#.
..?.#
.#.#.
..#..
Depth -4:
...#.
...##
..?..
...##
...#.
Depth -3:
#.#..
.#...
..?..
.#...
#.#..
Depth -2:
.#.##
....#
..?.#
...##
.###.
Depth -1:
#..##
...##
..?..
...#.
.####
Depth 0:
.#...
.#.##
.#?..
.....
.....
Depth 1:
.##..
#..##
..?.#
##.##
#####
Depth 2:
###..
##.#.
#.?..
.#.##
#.#..
Depth 3:
..###
.....
#.?..
#....
#...#
Depth 4:
.###.
#..#.
#.?..
##.#.
.....
Depth 5:
####.
#..#.
#.?#.
####.
.....
In this example, after 10 minutes, a total of [1m[97m99[0m bugs are present.
Starting with your scan, [1m[97mhow many bugs are present after 200 minutes?[0m
|
