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--- Day 21: Fractal Art ---
You find a program trying to generate some art. It uses a strange process that involves repeatedly enhancing the detail of an image through a set of rules.
The image consists of a two-dimensional square grid of pixels that are either on (#) or off (.). The program always begins with this pattern:
.#.
..#
###
Because the pattern is both 3 pixels wide and 3 pixels tall, it is said to have a size of 3.
Then, the program repeats the following process:
If the size is evenly divisible by 2, break the pixels up into 2x2 squares, and convert each 2x2 square into a 3x3 square by following the corresponding enhancement rule.
Otherwise, the size is evenly divisible by 3; break the pixels up into 3x3 squares, and convert each 3x3 square into a 4x4 square by following the corresponding enhancement rule.
Because each square of pixels is replaced by a larger one, the image gains pixels and so its size increases.
The artist's book of enhancement rules is nearby (your puzzle input); however, it seems to be missing rules. The artist explains that sometimes, one must rotate or flip the input pattern to find a match. (Never rotate or flip the output pattern, though.) Each pattern is written concisely: rows are listed as single units, ordered top-down, and separated by slashes. For example, the following rules correspond to the adjacent patterns:
../.# = ..
.#
.#.
.#./..#/### = ..#
###
#..#
#..#/..../#..#/.##. = ....
#..#
.##.
When searching for a rule to use, rotate and flip the pattern as necessary. For example, all of the following patterns match the same rule:
.#. .#. #.. ###
..# #.. #.# ..#
### ### ##. .#.
Suppose the book contained the following two rules:
../.# => ##./#../...
.#./..#/### => #..#/..../..../#..#
As before, the program begins with this pattern:
.#.
..#
###
The size of the grid (3) is not divisible by 2, but it is divisible by 3. It divides evenly into a single square; the square matches the second rule, which produces:
#..#
....
....
#..#
The size of this enhanced grid (4) is evenly divisible by 2, so that rule is used. It divides evenly into four squares:
#.|.#
..|..
--+--
..|..
#.|.#
Each of these squares matches the same rule (../.# => ##./#../...), three of which require some flipping and rotation to line up with the rule. The output for the rule is the same in all four cases:
##.|##.
#..|#..
...|...
---+---
##.|##.
#..|#..
...|...
Finally, the squares are joined into a new grid:
##.##.
#..#..
......
##.##.
#..#..
......
Thus, after 2 iterations, the grid contains 12 pixels that are on.
How many pixels stay on after 5 iterations?
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