Saturday, December 20, 2008

ark2 methuselah

This Conway game of Life pattern (probably) stabilizes at generation 8120878.

# ark2 -- 19 cells, stabilizes somewhere between 2^22 and 2^23 gens,
# found by Nick Gotts.
x = 53, y = 44, rule = B3/S23
50b3o28$12bo$12bo$13boo$15bo$15bo$15bo$15bo6$oo$bbo$bbo$3b4o!

The ark is a pair of switch engines leaving a considerable trail of debris. ("Two of everything"; perhaps that is why it is called "ark"?). It is a double-barreled backwards rake which continually perturbs the "tail" end of the debris trail.

A forward glider emitted by the debris "tail" collides with the ark at generation 4900986 in the neighborhood of (408454,408400). This kills half of the ark, converting it into a block-laying switch engine which (I think) escapes. Debris from this collision includes backwards gliders, one of which collides with another forward glider from the debris tail in the neighborhood of (401514, 401721) at generation 4932611 producing (via a pi heptomino) a small debris pile in that area. Another forward glider ("the last glider") from the tail collides with this small debris pile at generation 8120769 and everything stabilizes at 8120878.

There are other debris piles formed similarly, for example around (314700,314700) near generation 5700000, so there might be another glider bouncing up and down because of one, or another active debris pile, so I'm not completely sure that the pattern has stabilized.

Incidentally, the final "authentic" backward glider emitted by the ark rake reaches the tail at around generation 6526000.

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