Results of running the pattern in Golly:Jormungant wrote: April 15th, 2023, 5:49 am So, here is a pattern that grows as O(t^(2/3)):The above will send groups of corderships, and group sizes matches the following sequence: 1,2,1,3,1,4,1,5,1,6,1,7 etc. This is how the pattern grows, but I would just reiterate on why this translates to be t^2/3 growth, now that I have some visual props to support it.Code: Select all
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(...)
Code: Select all
T = generation, p = population, p = k * T^(2/3)
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T = 10^6 p = 27,568 k ~ 2,76
T = 10^7 p = 89,504 k ~ 1,93
T = 10^8 p = 532,200 k ~ 2,47
T = 10^9 p = 3,074,896 k ~ 3,07
T = 10^10 p = 16,338,234 k ~ 3,52
T = 10^11 p = 81,203,953 k ~ 3,77
T = 10^12 p = 389,163,948 k ~ 3,89
T = 10^13 p = 1,834,781,232 k ~ 3,95
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Code: Select all
3 2
256 n + 26880 n + 40448 n - 50250
-----------------------------------
3
Edit: for the quartic_root_growth.rle.gz pattern, the "singular" appearances of the input Herschel of the converter are at T = 5716, 74455, 200407, 402647, 701143, 1116375, ... The population at these times should be 24013 + (the total population of all already sent Corderships).
Code: Select all
4 3 2
64 n + 9088 n + 29120 n + 55424 n - 77691
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3
