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In Conway's Game of Life, there is an infinite square grid of cells, each of which is alive or dead. The pattern changes each "generation". A dead cell with exactly 3 live neighbors (orthogonal or diagonal) becomes a live cell. A live cell only lives to the next generation if it has 2 or 3 live neighbors. These simple rules lead to very complex behaviors. The most well-known pattern is the glider, a pattern that moves diagonally one cell every 4 generations and looks like this:

A Glider

The Challenge

Your task is to create two patterns which will eventually result in an empty board when by themselves (a.k.a. a diehard), but when combined in a certain non-bordering and non-overlapping arrangement, eventually spawn a single glider and nothing else.

Rules and Scoring

  • Each of the lone diehards must fit all live cells within a 100x100 cell box and may not contain more than 100 live cells.
  • The combination glider synthesizer must contain both diehards such that their bounding boxes surrounding all live cells are separated by at least one dead cell.
  • It does not matter which direction the single glider is facing
  • Your score is the sum of the number of generations it takes to reach an empty board from the initial states for the diehards, plus the number of generations it takes to reach a state where there is exactly one glider and nothing else (i.e. there are exactly 5 live cells on the board in a glider pattern) for the combined glider synthesizer. Highest score wins.
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  • \$\begingroup\$ By the three initial patterns, you mean time it takes for diehard 1 to disappear + time it takes for diehard 2 to disappear + time it takes their combination to create a single glider? \$\endgroup\$
    – Cloudy7
    Mar 26 at 16:12
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    \$\begingroup\$ @Cloudy7 you are mostly correct, though with the glider synthesizer, the end state is when there is exactly one glider somewhere and no other live cells. \$\endgroup\$
    – Beefster
    Mar 26 at 16:30
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    \$\begingroup\$ I wish I had thought of this sooner, but if you're a fan of the films (or silliness in general), you could call this "Die Hard 2: Glide Harder" :) \$\endgroup\$ Mar 26 at 16:41
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    \$\begingroup\$ @FryAmTheEggman "Now I have a machine gun! Ho-ho-ho." \$\endgroup\$
    – Arnauld
    Mar 26 at 17:01
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Total Score 669 683 753

Pattern 1 (379 steps):

x = 100, y = 94
97b2o$96bo2bo$97bobo$98bo$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$3o$2bo$bo!

Pattern 2 (126 steps):

x = 11, y = 2
o5b2obo$3bo$2b2o2bo2b2o!

Pattern 1 + Pattern 2 (248 steps):

x = 112, y = 94
97b2o$96bo2bo$97bobo$98bo2bo5b2obo$104bo$103b2o2bo2b2o$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$3o$2bo$bo!

Pattern 1 is a self-destructing glider + loaf combination where the glider and loaf are spaced as far apart as possible.

Pattern 2 is the result of searching for random disappearing patterns which can be placed next to pattern 1 to destroy the loaf, giving a valid solution to the puzzle. I generated a large number and took the one with the best score.

I'm sure its possible to do better by adding an independent diehard to the far corner of pattern 2 (or even pattern 1), but I'm done for now.

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    \$\begingroup\$ Just an FYI, you can include links to the starting patterns on copy.sh by creating gists of the pattern files, then linking to copy.sh/life?gist={gist id} where {gist id} can be found in the URL for the gist. For example, the id of https://gist.github.com/cairdcoinheringaahing/bac8f1088a10bfd835ba3309feddd016 is bac8f1088a10bfd835ba3309feddd016. Hope this helps! \$\endgroup\$ Mar 29 at 14:08
  • \$\begingroup\$ Could you add some images so we can see what the patterns look like? \$\endgroup\$
    – Beefster
    Mar 29 at 15:37
  • \$\begingroup\$ @ChartZBelatedly OK, done. \$\endgroup\$ Mar 29 at 17:29

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