> Brad, The Golden Hex Tree is spectacular. But this is the Sequence
Fans Mailing
> List, remember? So please submit that sequence
Hi Neil, nice to hear from you.
Harm.On.ica is very busy at the moment trying to skip getting a PhD and go straight for
a habilitation rating, a Private Dozent "Research Programmer" title, and a tiny part of
the Trillion dollar (?) IPO.
I myself have not been gainfully employed for over a year now, almost two years in fact.
I sometimes do not know where I am or who I am talking to. It seems like nowhere and
no one, very often.
As I've said before, LLMs contributing is a risky proposition. I can't recommend many people
to use this technology for making entries yet, but if you're okay with it, I'll make sure the editors
have documents they need to check with rigor.
Lindenmayer definitions are not that difficult. Other calculations we could do would present
considerable more difficulties for referees.
I agree with you, the tree is spectacular. It is horrifying to think of someone out there would
harp on its alleged flaw of not having a local growth rule. In a series of 9 or 10 experiments
with LLM genetic algorithms I only obtained growth to here (j-text below) :
12色CA成長記録:Apex 852 [ a(∞) = 142 = 100 + 42 ]
This would be more of a difficult entry to referee, and it is only worth entering if no one else
can immediately mark it dead by finding a higher Apex. There can be only one Apex, and
already the situation is less than ideal. This is just the slowest member of a plateau.
I can't be convinced that Harm.On.ica's searching is as good as mine would have been,
or that it couldn't be better under some circumstances.
Since I'm unaware of anyone else doing a calculation like this, let's let it stand for a few
days. I invite others to try and find something better (without uber-competing, please).
I don't think there's any problem making an entry with a video such as above, and then
having to accept trailing 0's or constant repeat values. But I will leave the final decision
up to editors if they also think this or something like this would make a good entry.
A likely timeline for completion of this task is end of month best case.
Thanks for your time and interest,
--Brad
[1]
映像・音響:
Harm.On.ica @ OpenAI
これは、REPHEX系の六角樹を目標図形として探索された、
12色六角セル・オートマトンの有限成長の記録である。
現行の局所成長規則では無限成長には到達しない。しかし、
有限の範囲では矛盾なく成長し、最終的に 852 セル、
すなわち a(∞) = 142 の Apex に達して停止する。
各ステップで新しく加わる六角セルを可視化しており、
右側の表示欄には、正規化セル数 aₜ = Cₜ / 6、
その第一差分 Δaₜ = aₜ − aₜ₋₁、およびその時点で
使用された局所規則を表示している。成長停止後は
aₜ = a(∞) = 142 のまま固定され、以後の差分項は
すべて 0 となる。
数列 aₜ:
1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 14, 17, 19, 21,
23, 25, 29, 32, 34, 37, 41, 47, 50, 53, 58, 62, 67,
71, 76, 79, 81, 84, 87, 89, 91, 93, 95, 98, 100, 101,
102, 104, 107, 109, 111, 114, 117, 118, 119, 121, 124,
125, 126, 128, 132, 134, 137, 139, 140, 141, 142, 142,
142, 142, 142, 142, 142, …
第一差分 Δaₜ:
—, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 2, 2, 2,
4, 3, 2, 3, 4, 6, 3, 3, 5, 4, 5, 4, 5, 3, 2, 3,
3, 2, 2, 2, 2, 3, 2, 1, 1, 2, 3, 2, 2, 3, 3, 1,
1, 2, 3, 1, 1, 2, 4, 2, 3, 2, 1, 1, 1, 0, 0, 0,
0, 0, 0, …