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Add problem statements and inputs
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 09 Jan 2018 21:51:44 -0500
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1 --- Day 21: Fractal Art ---
2
3 You find a program trying to generate some art. It uses a strange
4 process that involves repeatedly enhancing the detail of an image
5 through a set of rules.
6
7 The image consists of a two-dimensional square grid of pixels that are
8 either on (#) or off (.). The program always begins with this pattern:
9
10 .#.
11 ..#
12 ###
13
14 Because the pattern is both 3 pixels wide and 3 pixels tall, it is
15 said to have a size of 3.
16
17 Then, the program repeats the following process:
18
19 If the size is evenly divisible by 2, break the pixels up into 2x2
20 squares, and convert each 2x2 square into a 3x3 square by
21 following the corresponding enhancement rule.
22
23 Otherwise, the size is evenly divisible by 3; break the pixels up
24 into 3x3 squares, and convert each 3x3 square into a 4x4 square by
25 following the corresponding enhancement rule.
26
27
28 Because each square of pixels is replaced by a larger one, the image
29 gains pixels and so its size increases.
30
31 The artist's book of enhancement rules is nearby (your puzzle input);
32 however, it seems to be missing rules. The artist explains that
33 sometimes, one must rotate or flip the input pattern to find a match.
34 (Never rotate or flip the output pattern, though.) Each pattern is
35 written concisely: rows are listed as single units, ordered top-down,
36 and separated by slashes. For example, the following rules correspond
37 to the adjacent patterns:
38
39 ../.# = ..
40 .#
41
42 .#.
43 .#./..#/### = ..#
44 ###
45
46 #..#
47 #..#/..../#..#/.##. = ....
48 #..#
49 .##.
50
51 When searching for a rule to use, rotate and flip the pattern as
52 necessary. For example, all of the following patterns match the same
53 rule:
54
55 .#. .#. #.. ###
56 ..# #.. #.# ..#
57 ### ### ##. .#.
58
59 Suppose the book contained the following two rules:
60
61 ../.# => ##./#../...
62 .#./..#/### => #..#/..../..../#..#
63
64 As before, the program begins with this pattern:
65
66 .#.
67 ..#
68 ###
69
70 The size of the grid (3) is not divisible by 2, but it is divisible by
71 3. It divides evenly into a single square; the square matches the
72 second rule, which produces:
73
74 #..#
75 ....
76 ....
77 #..#
78
79 The size of this enhanced grid (4) is evenly divisible by 2, so that
80 rule is used. It divides evenly into four squares:
81
82 #.|.#
83 ..|..
84 --+--
85 ..|..
86 #.|.#
87
88 Each of these squares matches the same rule (../.# => ##./#../...),
89 three of which require some flipping and rotation to line up with the
90 rule. The output for the rule is the same in all four cases:
91
92 ##.|##.
93 #..|#..
94 ...|...
95 ---+---
96 ##.|##.
97 #..|#..
98 ...|...
99
100 Finally, the squares are joined into a new grid:
101
102 ##.##.
103 #..#..
104 ......
105 ##.##.
106 #..#..
107 ......
108
109 Thus, after 2 iterations, the grid contains 12 pixels that are on.
110
111 How many pixels stay on after 5 iterations?
112
113 Your puzzle answer was 176.
114
115 --- Part Two ---
116
117 How many pixels stay on after 18 iterations?
118
119 Your puzzle answer was 2368161.
120
121 Both parts of this puzzle are complete! They provide two gold stars: **