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diff --git a/src/2017/day21/README.md b/src/2017/day21/README.md index e69de29..31e7817 100644 --- a/src/2017/day21/README.md +++ b/src/2017/day21/README.md @@ -0,0 +1,77 @@ +--- 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? + |