part2 (3027B)
1--- Part Two --- 2 3For some reason, your simulated results don't match what the experimental energy source engineers 4expected. Apparently, the pocket dimension actually has [1m[37mfour spatial dimensions[0m, not 5three. 6 7The pocket dimension contains an infinite 4-dimensional grid. At every integer 4-dimensional 8coordinate (x,y,z,w), there exists a single cube (really, a [1m[37mhypercube[0m) which is still 9either [1m[37mactive[0m or [1m[37minactive[0m. 10 11Each cube only ever considers its [1m[37mneighbors[0m: any of the 80 other cubes where any of 12their coordinates differ by at most 1. For example, given the cube at x=1,y=2,z=3,w=4, its neighbors 13include 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. 14 15The initial state of the pocket dimension still consists of a small flat region of cubes. 16Furthermore, the same rules for cycle updating still apply: during each cycle, consider the 17[1m[37mnumber of active neighbors[0m of each cube. 18 19For example, consider the same initial state as in the example above. Even though the pocket 20dimension is 4-dimensional, this initial state represents a small 2-dimensional slice of it. (In 21particular, this initial state defines a 3x3x1x1 region of the 4-dimensional space.) 22 23Simulating a few cycles from this initial state produces the following configurations, where the 24result of each cycle is shown layer-by-layer at each given z and w coordinate: 25 26Before any cycles: 27 28z=0, w=0 29.#. 30..# 31### 32 33 34After 1 cycle: 35 36z=-1, w=-1 37#.. 38..# 39.#. 40 41z=0, w=-1 42#.. 43..# 44.#. 45 46z=1, w=-1 47#.. 48..# 49.#. 50 51z=-1, w=0 52#.. 53..# 54.#. 55 56z=0, w=0 57#.# 58.## 59.#. 60 61z=1, w=0 62#.. 63..# 64.#. 65 66z=-1, w=1 67#.. 68..# 69.#. 70 71z=0, w=1 72#.. 73..# 74.#. 75 76z=1, w=1 77#.. 78..# 79.#. 80 81 82After 2 cycles: 83 84z=-2, w=-2 85..... 86..... 87..#.. 88..... 89..... 90 91z=-1, w=-2 92..... 93..... 94..... 95..... 96..... 97 98z=0, w=-2 99###.. 100##.## 101#...# 102.#..# 103.###. 104 105z=1, w=-2 106..... 107..... 108..... 109..... 110..... 111 112z=2, w=-2 113..... 114..... 115..#.. 116..... 117..... 118 119z=-2, w=-1 120..... 121..... 122..... 123..... 124..... 125 126z=-1, w=-1 127..... 128..... 129..... 130..... 131..... 132 133z=0, w=-1 134..... 135..... 136..... 137..... 138..... 139 140z=1, w=-1 141..... 142..... 143..... 144..... 145..... 146 147z=2, w=-1 148..... 149..... 150..... 151..... 152..... 153 154z=-2, w=0 155###.. 156##.## 157#...# 158.#..# 159.###. 160 161z=-1, w=0 162..... 163..... 164..... 165..... 166..... 167 168z=0, w=0 169..... 170..... 171..... 172..... 173..... 174 175z=1, w=0 176..... 177..... 178..... 179..... 180..... 181 182z=2, w=0 183###.. 184##.## 185#...# 186.#..# 187.###. 188 189z=-2, w=1 190..... 191..... 192..... 193..... 194..... 195 196z=-1, w=1 197..... 198..... 199..... 200..... 201..... 202 203z=0, w=1 204..... 205..... 206..... 207..... 208..... 209 210z=1, w=1 211..... 212..... 213..... 214..... 215..... 216 217z=2, w=1 218..... 219..... 220..... 221..... 222..... 223 224z=-2, w=2 225..... 226..... 227..#.. 228..... 229..... 230 231z=-1, w=2 232..... 233..... 234..... 235..... 236..... 237 238z=0, w=2 239###.. 240##.## 241#...# 242.#..# 243.###. 244 245z=1, w=2 246..... 247..... 248..... 249..... 250..... 251 252z=2, w=2 253..... 254..... 255..#.. 256..... 257..... 258 259After the full six-cycle boot process completes, [1m[37m848[0m cubes are left in the 260[1m[37mactive[0m state. 261 262Starting with your given initial configuration, simulate six cycles in a 4-dimensional space. 263[1m[37mHow many cubes are left in the active state after the sixth cycle?[0m 264 265