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diff --git a/src/17/part2 b/src/17/part2 new file mode 100644 index 0000000..a824996 --- /dev/null +++ b/src/17/part2 @@ -0,0 +1,265 @@ +--- Part Two --- + +For some reason, your simulated results don't match what the experimental energy source engineers +expected. Apparently, the pocket dimension actually has [1m[37mfour spatial dimensions[0m, 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 [1m[37mhypercube[0m) which is still +either [1m[37mactive[0m or [1m[37minactive[0m. + +Each cube only ever considers its [1m[37mneighbors[0m: 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 +[1m[37mnumber of active neighbors[0m 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: + +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, [1m[37m848[0m cubes are left in the +[1m[37mactive[0m state. + +Starting with your given initial configuration, simulate six cycles in a 4-dimensional space. +[1m[37mHow many cubes are left in the active state after the sixth cycle?[0m + + |