day17: Day 17: Conway Cubes
In tjmahr/adventofcode20: Advent of Code 2020
Description
Usage
Arguments
Details
Value
Examples
Description
Usage
1
2
3
run_conway_cube(x, dim = "3d", messages = FALSE)
example_cube_state(example = 1)
Arguments
x
Starting plane for a Conway cube.
dim
Dimension setting. Either "3d" or "4d".
messages
Whether to message on the start of each iteration.
example
which example data to use. Defaults to 1.
Details
Part One
Information Bureau at the North Pole contact you. They'd like some help
debugging a malfunctioning experimental energy source aboard one of
their super-secret imaging satellites.
The experimental energy source is based on cutting-edge technology: a
set of [Conway]title="Rest in peace, Conway." Cubes contained in a
pocket dimension! When you hear it's having problems, you can't help
but agree to take a look.
The pocket dimension contains an infinite 3-dimensional grid. At every
integer 3-dimensional coordinate (x,y,z), there exists a single cube
which is either active or inactive.
In the initial state of the pocket dimension, almost all cubes start
inactive. The only exception to this is a small flat region of cubes
(your puzzle input); the cubes in this region start in the specified
active (#) or inactive (.) state.
The energy source then proceeds to boot up by executing six cycles.
Each cube only ever considers its neighbors: any of the 26 other cubes
where any of their coordinates differ by at most 1. For example, given
the cube at x=1,y=2,z=3, its neighbors include the cube at
x=2,y=2,z=2, the cube at x=0,y=2,z=3, and so on.
During a cycle, all cubes simultaneously change their state
according to the following rules:
If a cube is active and exactly 2 or 3 of its neighbors are
also active, the cube remains active. Otherwise, the cube becomes
inactive.
If a cube is inactive but exactly 3 of its neighbors are
active, the cube becomes active. Otherwise, the cube remains
inactive.
The engineers responsible for this experimental energy source would like
you to simulate the pocket dimension and determine what the
configuration of cubes should be at the end of the six-cycle boot
process.
For example, consider the following initial state:
1
2
3
.#.
..#
###
Even though the pocket dimension is 3-dimensional, this initial state
represents a small 2-dimensional slice of it. (In particular, this
initial state defines a 3x3x1 region of the 3-dimensional space.)
Simulating a few cycles from this initial state produces the following
configurations, where the result of each cycle is shown layer-by-layer
at each given z coordinate (and the frame of view follows the active
cells in each cycle):
1
2
3
4
5
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Before any cycles:
z=0
.#.
..#
###
After 1 cycle:
z=-1
#..
..#
.#.
z=0
#.#
.##
.#.
z=1
#..
..#
.#.
After 2 cycles:
z=-2
.....
.....
..#..
.....
.....
z=-1
..#..
.#..#
....#
.#...
.....
z=0
##...
##...
#....
....#
.###.
z=1
..#..
.#..#
....#
.#...
.....
z=2
.....
.....
..#..
.....
.....
After 3 cycles:
z=-2
.......
.......
..##...
..###..
.......
.......
.......
z=-1
..#....
...#...
#......
.....##
.#...#.
..#.#..
...#...
z=0
...#...
.......
#......
.......
.....##
.##.#..
...#...
z=1
..#....
...#...
#......
.....##
.#...#.
..#.#..
...#...
z=2
.......
.......
..##...
..###..
.......
.......
.......
After the full six-cycle boot process completes, 112 cubes are left
in the active state.
Starting with your given initial configuration, simulate six cycles.
How many cubes are left in the active state after the sixth cycle?
Part Two
For some reason, your simulated results don\'t match what the
experimental energy source engineers expected. Apparently, the pocket
dimension actually has four spatial dimensions, not three.
The pocket dimension contains an infinite 4-dimensional grid. At every
integer 4-dimensional coordinate (x,y,z,w), there exists a single cube
(really, a hypercube) which is still either active or inactive.
Each cube only ever considers its neighbors: any of the 80 other cubes
where any of their coordinates differ by at most 1. For example, given
the cube at x=1,y=2,z=3,w=4, its neighbors include the cube at
x=2,y=2,z=3,w=3, the cube at x=0,y=2,z=3,w=4, and so on.
The initial state of the pocket dimension still consists of a small flat
region of cubes. Furthermore, the same rules for cycle updating still
apply: during each cycle, consider the number of active neighbors of
each cube.
For example, consider the same initial state as in the example above.
Even though the pocket dimension is 4-dimensional, this initial state
represents a small 2-dimensional slice of it. (In particular, this
initial state defines a 3x3x1x1 region of the 4-dimensional space.)
Simulating a few cycles from this initial state produces the following
configurations, where the result of each cycle is shown layer-by-layer
at each given z and w coordinate:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
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Before any cycles:
z=0, w=0
.#.
..#
###
After 1 cycle:
z=-1, w=-1
#..
..#
.#.
z=0, w=-1
#..
..#
.#.
z=1, w=-1
#..
..#
.#.
z=-1, w=0
#..
..#
.#.
z=0, w=0
#.#
.##
.#.
z=1, w=0
#..
..#
.#.
z=-1, w=1
#..
..#
.#.
z=0, w=1
#..
..#
.#.
z=1, w=1
#..
..#
.#.
After 2 cycles:
z=-2, w=-2
.....
.....
..#..
.....
.....
z=-1, w=-2
.....
.....
.....
.....
.....
z=0, w=-2
###..
##.##
#...#
.#..#
.###.
z=1, w=-2
.....
.....
.....
.....
.....
z=2, w=-2
.....
.....
..#..
.....
.....
z=-2, w=-1
.....
.....
.....
.....
.....
z=-1, w=-1
.....
.....
.....
.....
.....
z=0, w=-1
.....
.....
.....
.....
.....
z=1, w=-1
.....
.....
.....
.....
.....
z=2, w=-1
.....
.....
.....
.....
.....
z=-2, w=0
###..
##.##
#...#
.#..#
.###.
z=-1, w=0
.....
.....
.....
.....
.....
z=0, w=0
.....
.....
.....
.....
.....
z=1, w=0
.....
.....
.....
.....
.....
z=2, w=0
###..
##.##
#...#
.#..#
.###.
z=-2, w=1
.....
.....
.....
.....
.....
z=-1, w=1
.....
.....
.....
.....
.....
z=0, w=1
.....
.....
.....
.....
.....
z=1, w=1
.....
.....
.....
.....
.....
z=2, w=1
.....
.....
.....
.....
.....
z=-2, w=2
.....
.....
..#..
.....
.....
z=-1, w=2
.....
.....
.....
.....
.....
z=0, w=2
###..
##.##
#...#
.#..#
.###.
z=1, w=2
.....
.....
.....
.....
.....
z=2, w=2
.....
.....
..#..
.....
.....
After the full six-cycle boot process completes, 848 cubes are left
in the active state.
Starting with your given initial configuration, simulate six cycles in a
4-dimensional space. How many cubes are left in the active state after
the sixth cycle?
Value
run_conway_cube(x) returns a dataframe with one row per cube. The
"value" column should sum to the solution.
Examples
1
tjmahr/adventofcode20 documentation built on Dec. 31, 2020, 8:39 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Value Examples
Description
Usage
1 2 3 | run_conway_cube(x, dim = "3d", messages = FALSE)
example_cube_state(example = 1)
|
Arguments
x |
Starting plane for a Conway cube. |
dim |
Dimension setting. Either |
messages |
Whether to message on the start of each iteration. |
example |
which example data to use. Defaults to 1. |
Details
Part One
Information Bureau at the North Pole contact you. They'd like some help debugging a malfunctioning experimental energy source aboard one of their super-secret imaging satellites.
The experimental energy source is based on cutting-edge technology: a set of [Conway]title="Rest in peace, Conway." Cubes contained in a pocket dimension! When you hear it's having problems, you can't help but agree to take a look.
The pocket dimension contains an infinite 3-dimensional grid. At every
integer 3-dimensional coordinate (x,y,z), there exists a single cube
which is either active or inactive.
In the initial state of the pocket dimension, almost all cubes start
inactive. The only exception to this is a small flat region of cubes
(your puzzle input); the cubes in this region start in the specified
active (#) or inactive (.) state.
The energy source then proceeds to boot up by executing six cycles.
Each cube only ever considers its neighbors: any of the 26 other cubes
where any of their coordinates differ by at most 1. For example, given
the cube at x=1,y=2,z=3, its neighbors include the cube at
x=2,y=2,z=2, the cube at x=0,y=2,z=3, and so on.
During a cycle, all cubes simultaneously change their state according to the following rules:
If a cube is active and exactly
2or3of its neighbors are also active, the cube remains active. Otherwise, the cube becomes inactive.If a cube is inactive but exactly
3of its neighbors are active, the cube becomes active. Otherwise, the cube remains inactive.
The engineers responsible for this experimental energy source would like you to simulate the pocket dimension and determine what the configuration of cubes should be at the end of the six-cycle boot process.
For example, consider the following initial state:
1 2 3 | .#.
..#
###
|
Even though the pocket dimension is 3-dimensional, this initial state represents a small 2-dimensional slice of it. (In particular, this initial state defines a 3x3x1 region of the 3-dimensional space.)
Simulating a few cycles from this initial state produces the following
configurations, where the result of each cycle is shown layer-by-layer
at each given z coordinate (and the frame of view follows the active
cells in each cycle):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 | Before any cycles:
z=0
.#.
..#
###
After 1 cycle:
z=-1
#..
..#
.#.
z=0
#.#
.##
.#.
z=1
#..
..#
.#.
After 2 cycles:
z=-2
.....
.....
..#..
.....
.....
z=-1
..#..
.#..#
....#
.#...
.....
z=0
##...
##...
#....
....#
.###.
z=1
..#..
.#..#
....#
.#...
.....
z=2
.....
.....
..#..
.....
.....
After 3 cycles:
z=-2
.......
.......
..##...
..###..
.......
.......
.......
z=-1
..#....
...#...
#......
.....##
.#...#.
..#.#..
...#...
z=0
...#...
.......
#......
.......
.....##
.##.#..
...#...
z=1
..#....
...#...
#......
.....##
.#...#.
..#.#..
...#...
z=2
.......
.......
..##...
..###..
.......
.......
.......
|
After the full six-cycle boot process completes, 112 cubes are left
in the active state.
Starting with your given initial configuration, simulate six cycles. How many cubes are left in the active state after the sixth cycle?
Part Two
For some reason, your simulated results don\'t match what the experimental energy source engineers expected. Apparently, the pocket dimension actually has four spatial dimensions, not three.
The pocket dimension contains an infinite 4-dimensional grid. At every
integer 4-dimensional coordinate (x,y,z,w), there exists a single cube
(really, a hypercube) which is still either active or inactive.
Each cube only ever considers its neighbors: any of the 80 other cubes
where any of their coordinates differ by at most 1. For example, given
the cube at x=1,y=2,z=3,w=4, its neighbors include the cube at
x=2,y=2,z=3,w=3, the cube at x=0,y=2,z=3,w=4, and so on.
The initial state of the pocket dimension still consists of a small flat region of cubes. Furthermore, the same rules for cycle updating still apply: during each cycle, consider the number of active neighbors of each cube.
For example, consider the same initial state as in the example above. Even though the pocket dimension is 4-dimensional, this initial state represents a small 2-dimensional slice of it. (In particular, this initial state defines a 3x3x1x1 region of the 4-dimensional space.)
Simulating a few cycles from this initial state produces the following
configurations, where the result of each cycle is shown layer-by-layer
at each given z and w coordinate:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 | Before any cycles:
z=0, w=0
.#.
..#
###
After 1 cycle:
z=-1, w=-1
#..
..#
.#.
z=0, w=-1
#..
..#
.#.
z=1, w=-1
#..
..#
.#.
z=-1, w=0
#..
..#
.#.
z=0, w=0
#.#
.##
.#.
z=1, w=0
#..
..#
.#.
z=-1, w=1
#..
..#
.#.
z=0, w=1
#..
..#
.#.
z=1, w=1
#..
..#
.#.
After 2 cycles:
z=-2, w=-2
.....
.....
..#..
.....
.....
z=-1, w=-2
.....
.....
.....
.....
.....
z=0, w=-2
###..
##.##
#...#
.#..#
.###.
z=1, w=-2
.....
.....
.....
.....
.....
z=2, w=-2
.....
.....
..#..
.....
.....
z=-2, w=-1
.....
.....
.....
.....
.....
z=-1, w=-1
.....
.....
.....
.....
.....
z=0, w=-1
.....
.....
.....
.....
.....
z=1, w=-1
.....
.....
.....
.....
.....
z=2, w=-1
.....
.....
.....
.....
.....
z=-2, w=0
###..
##.##
#...#
.#..#
.###.
z=-1, w=0
.....
.....
.....
.....
.....
z=0, w=0
.....
.....
.....
.....
.....
z=1, w=0
.....
.....
.....
.....
.....
z=2, w=0
###..
##.##
#...#
.#..#
.###.
z=-2, w=1
.....
.....
.....
.....
.....
z=-1, w=1
.....
.....
.....
.....
.....
z=0, w=1
.....
.....
.....
.....
.....
z=1, w=1
.....
.....
.....
.....
.....
z=2, w=1
.....
.....
.....
.....
.....
z=-2, w=2
.....
.....
..#..
.....
.....
z=-1, w=2
.....
.....
.....
.....
.....
z=0, w=2
###..
##.##
#...#
.#..#
.###.
z=1, w=2
.....
.....
.....
.....
.....
z=2, w=2
.....
.....
..#..
.....
.....
|
After the full six-cycle boot process completes, 848 cubes are left
in the active state.
Starting with your given initial configuration, simulate six cycles in a 4-dimensional space. How many cubes are left in the active state after the sixth cycle?
Value
run_conway_cube(x) returns a dataframe with one row per cube. The
"value" column should sum to the solution.
Examples
1 |
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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