I like the MCPS metric as a measure of size, but I'm not sure about L/MCPS as a measure of methuselahiness. It seems easy to game. In the same way that a glider aimed at a block does well for L/P, a simple semisnark chain does well for L/MCPS.calcyman wrote:Well, if longevity were more important than bounding box, it would be trumped by a glider aimed at a very distant blinker. I like Oscar's L/MCPS metric, which gives a ratio of 1283.4 for 47487M. Again, the longest-lived methuselah which beats that is simeks' remarkable 9x6 Lidka variant (1941.7).
If we had a smooth function f such that the lifespan of the best methuselahs was approximately f(MCPS) then we could judge methuselahs by a metric like MCPS - f^-1(L). But given that we know that such an f has to grow uncomputably quickly, I don't think we'll ever be able to practically use a method like this.
I'd rather just describe a partial order: a pattern is a better methuselah if it has both a longer lifespan and a smaller MCPS. Then we can say that the record methuselahs are the ones on the Pareto frontier, without trying to compare between them by boiling them down to a single number. By these standards the best methuselahs are currently
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Name MCPS L Bit 1 1 obo2$bo! 3 2 bo2$3o! 4 11 R-pentomino grandparents 5 1105 Multum in parvo 7 3933 Acorn 8 5206 7468M 9 7468 Rabbits 10 17331 Bunnies 11 17332 Bunnies 11 12 17465 18034M 13 18034 23334M 14 23334 Lidka predecessor 15 29126 Eve 26 30046 47575M variant 37 47487 47575M 132 47575 ??? Recursive filter <20000 >2→2→3→6