We're given a grid based cellular automata with a couple of complications:
- We need to be able to split the grid into either 2x2 or 3x3 subgrids, apply rules and then recombine.
- We need to apply rules from a given ruleset, which includes rotating and flipping the input rules if needed.
This was a good exercise to get more familiar with NumPy. The most difficult part was splitting a grid into subgrids.
I imagined stacking up the 2x2 grids in a say, 32 grid by reshaping it:
matrix.reshape(-1, 2, 2) should create a 3d matrix of 2x2 matricies, with
the 3rd dimension being whatever it needs to be (-1 tells numpy to figure
out). Unfortunately, this stacks the first 4 numbers of the first row into
the first layer, instead of taking a 2x2 sub-grid.
I could have written a for loop extracting these using slices, but it didn't
seem very efficient. I searched online for a solution and found
blockshaped, which pulls out the subgrids by reshaping to a 4d, then 3d
array.
One other trick that was needed was using numpy arrays as dictionary keys.
They're not hashable, so I needed to use .tobytes() to turn them into
something hashable.
Overall, this worked very well. Going forward, I hope to use numpy for advent of code more often.
2017 Day 21 on AdventOfCode.com
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?
How many pixels stay on after 18 iterations?