## Wednesday, June 17, 2020

### [uggjzjou] Methuselah 2000

I like L/MCPS (lifespan / minimum covering polyplet size) as the measure of notability of methuselahs.  Sort the following table by L/MCPS,

https://conwaylife.com/w/index.php?title=List_of_long-lived_methuselahs&oldid=68826

, and the current maximum is "Lidka predecessor" with L/MCPS = 29126/15 = 1941.7 :

x = 9, y = 6, rule = LifeHistory
6.A\$6.3A2\$3.2A3.A\$3.A4.A\$3A5.A!

This begs a challenge of finding a methuselah with L/MCPS greater than 2000.

Methuselahs based on puffers (especially rakes) have been excluded from the table linked above.  However, Golly includes ark1 and ark2 in its Methuselahs directory.  I've also read somewhere (maybe Martin Gardner) Bill Gosper's very dirty B-heptomino puffer, the second puffer train ever discovered, being described as a methuselah, stabilizing at generation 5533.

Previously, we investigated ark2.  It has an initial population = 19, MCPS = 61 (or less), and Lifespan = 8120878 (or more).  Then, its L/MCPS >= 133129.1 .

This pattern by "TDiff?", from https://www.conwaylife.com/forums/viewtopic.php?f=2&t=3227#p55190 ,

x = 52, y = 57, rule = B3/S23
9b4o\$13bo\$13bo\$14b2o6\$o\$o\$o\$o\$b2o\$3bo\$3bo26\$48bo\$48bo\$49b2o\$51bo\$51bo\$
51bo\$51bo6\$36b2o\$38bo\$38bo\$39b4o!

stabilizes at around L = 127053473 or later (future post).  Its initial population is 32; its MCPS is less than or equal to 85 (draw diagonal bridges to connect components, pattern given below), so L/MCPS >= 1494746.7.

#CXRLE Pos=0,0
x = 52, y = 57, rule = B3/S23
9b4o\$8bo4bo\$7bo5bo\$6bo7b2o\$5bo\$4bo\$3bo\$2bo\$bo\$o\$o\$o\$o\$b2o\$3bo\$3bo\$4bo\$
4bo\$4bo\$4bo\$4bo\$4bo\$5bo\$6bo\$7bo\$8bo\$9bo\$10bo\$11bo\$12bo\$13bo\$14bo\$15bo\$
16bo\$17bo\$18bo\$19bo\$20bo\$21bo\$22bo\$23bo\$24bo23bo\$25bo22bo\$26bo22b2o\$
27bo23bo\$28bo22bo\$29bo21bo\$30bo20bo\$31bo18bo\$32bo16bo\$33bo14bo\$34bo12b
o\$35bo10bo\$36b2o7bo\$38bo5bo\$38bo4bo\$39b4o!

Is L/MCPS a fair measure of methuselah notability when puffers are allowed?  Maybe MCPS ought to be raised to an exponent.

Related investigations by Nick Gotts: http://nickgotts-eventful.blogspot.com