Sunday, June 28, 2020

[agnbukra] 127-million-generation ark methuselah in Conway's Game of Life

We investigate with Golly the following unnamed pattern by "TDiff?", from :

x = 52, y = 57, rule = B3/S23

The pattern consists of two arks (switch-engine based puffers) each producing exhaust which includes backward-traveling gliders.  The gliders interact with the exhaust.  Each ark produces two gliders every 768 generations.  One ark travels southeast (toward increasing X and Y coordinates) and the other travels northwest (toward decreasing X and Y coordinates).

The pattern has 180 degree rotational symmetry around the point (25.5, 27.5), so everything that happens in the southeast also happens identically in the northwest.  We report on activities in the southeast.

The southeast-traveling ark produces two parallel glider streams heading northwest.  The pattern will ultimately stabilize when two eaters form to consume the two glider streams.

We used Scripts/Lua/goto.lua to rapidly fast forward with the Hashlife algorithm then used binary search to find particular important generations.

At around generation 19400000, the reaction front, the frontier of where gliders interact with exhaust, passes where the second eater will be formed.  It might be fun to watch this region (coordinates of this second eater and the final fleet are given below) continuously from this timepoint onward, but Golly 3.3 kept freezing when we tried this at speed 8^1.

(It would be nice if Golly had a feature to automatically move the viewport to where interesting action is happening in a pattern like this, but there would be devilish details involved in doing this.  Perhaps rewind time if there are multiple hotspots.  It seems similar to TV coverage of a golf tournament.)

At around 97800000, the reaction front passes where the first eater will be formed.

At 98109317, the first eater configuration forms at (22554, 22478).  It is an OG eater (eater1, fishhook) but not in an orientation that cleanly eats gliders.  Every other glider, a boat forms next to it.  (This is an example of a "boat-bit".)  The boat gets destroyed by the next glider.  This eater configuration eats the upper glider stream emitted by the southeast-traveling rake.

At 127049301, the second eater configuration, a beacon, forms at (6790, 6876).  The glider stream penetrates quite far into the exhaust to reach this eater.  Every other glider, a boat forms next to the beacon, another example of a boat-bit.  The boat gets destroyed by the next glider.  This eater configuration eats the lower glider stream emitted by the southeast-traveling rake.

When this second eater forms, in its vicinity is an active region.  This region settles down at 127053473, producing a fleet at (6696, 6952).  We conjecture this is the last active region.  The population at this point is 105763948.  However, the population will continue to grow because the puffers (arks) keep going forever.

It's a little miraculous that gliders produced by the exhaust don't shoot down the puffers.  The puffers travel at speed c/12, much slower than gliders.  The puffers might be being shielded by their exhaust trails which are wider than the puffers.

To the south (and symmetrically north) escape 3 xWSS spaceships.  Starting from furthest south, they are: HWSS, LWSS, MWSS.  To the east (and symmetrically west) escape 9 xWSS spaceships.  Starting from furthest east, they are: LWSS, LWSS, MWSS, LWSS, LWSS, MWSS, LWSS, MWSS, MWSS.  Therefore, 24 xWSS escape in total.  Are there an unusually large proportion of spaceships that heavier than the lightweight spaceship?

For completeness, we also give important coordinates related to the northwest-traveling ark.  The first eater configuration (eater1) forms at (-22503, -22422).  The second eater configuration (beacon) forms at (-6739, -6820).  The final fleet forms at (-6646, -6901).

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