117 lines
3.1 KiB
Markdown
117 lines
3.1 KiB
Markdown
|
## \-\-- Day 21: Fractal Art \-\--
|
||
|
|
|
||
|
|
You find a program trying to generate some art. It uses a strange
|
||
|
|
process that involves [repeatedly
|
||
|
|
enhancing]{title="This technique is also often used on TV."} 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?
|
||
|
|
|
||
|
|
To begin, [get your puzzle input](21/input).
|
||
|
|
|
||
|
|
Answer:
|
||
|
|
|