130 lines
3.4 KiB
Markdown
130 lines
3.4 KiB
Markdown
## \-\-- Day 21: Fractal Art \-\--
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You find a program trying to generate some art. It uses a strange
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process that involves [repeatedly
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enhancing]{title="This technique is also often used on TV."} the detail
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of an image through a set of rules.
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The image consists of a two-dimensional square grid of pixels that are
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either on (`#`) or off (`.`). The program always begins with this
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pattern:
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.#.
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..#
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###
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Because the pattern is both `3` pixels wide and `3` pixels tall, it is
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said to have a *size* of `3`.
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Then, the program repeats the following process:
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- If the size is evenly divisible by `2`, break the pixels up into
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`2x2` squares, and convert each `2x2` square into a `3x3` square by
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following the corresponding *enhancement rule*.
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- Otherwise, the size is evenly divisible by `3`; break the pixels up
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into `3x3` squares, and convert each `3x3` square into a `4x4`
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square by following the corresponding *enhancement rule*.
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Because each square of pixels is replaced by a larger one, the image
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gains pixels and so its *size* increases.
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The artist\'s book of enhancement rules is nearby (your puzzle input);
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however, it seems to be missing rules. The artist explains that
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sometimes, one must *rotate* or *flip* the input pattern to find a
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match. (Never rotate or flip the output pattern, though.) Each pattern
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is written concisely: rows are listed as single units, ordered top-down,
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and separated by slashes. For example, the following rules correspond to
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the adjacent patterns:
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../.# = ..
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.#
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.#.
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.#./..#/### = ..#
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###
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#..#
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#..#/..../#..#/.##. = ....
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#..#
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.##.
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When searching for a rule to use, rotate and flip the pattern as
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necessary. For example, all of the following patterns match the same
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rule:
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.#. .#. #.. ###
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..# #.. #.# ..#
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### ### ##. .#.
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Suppose the book contained the following two rules:
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../.# => ##./#../...
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.#./..#/### => #..#/..../..../#..#
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As before, the program begins with this pattern:
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.#.
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..#
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###
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The size of the grid (`3`) is not divisible by `2`, but it is divisible
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by `3`. It divides evenly into a single square; the square matches the
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second rule, which produces:
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#..#
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....
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....
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#..#
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The size of this enhanced grid (`4`) is evenly divisible by `2`, so that
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rule is used. It divides evenly into four squares:
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#.|.#
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..|..
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--+--
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..|..
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#.|.#
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Each of these squares matches the same rule (`../.# => ##./#../...`),
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three of which require some flipping and rotation to line up with the
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rule. The output for the rule is the same in all four cases:
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##.|##.
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#..|#..
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...|...
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---+---
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##.|##.
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#..|#..
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...|...
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Finally, the squares are joined into a new grid:
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##.##.
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#..#..
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......
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##.##.
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#..#..
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......
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Thus, after `2` iterations, the grid contains `12` pixels that are *on*.
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*How many pixels stay on* after `5` iterations?
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Your puzzle answer was `162`.
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## \-\-- Part Two \-\-- {#part2}
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*How many pixels stay on* after `18` iterations?
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Your puzzle answer was `2264586`.
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Both parts of this puzzle are complete! They provide two gold stars:
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\*\*
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At this point, you should [return to your Advent calendar](/2017) and
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try another puzzle.
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If you still want to see it, you can [get your puzzle
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input](21/input).
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