콜라코프스키 수열

Kolakoski Sequence

26 pointsby surprisetalk2026. 2. 2.9 comments

원문 보기 (en.wikipedia.org)

요약

콜라코프스키 수열은 자신의 런-렝스 인코딩을 설명하는 {1,2} 기호의 무한 수열입니다. 수열의 각 항은 동일한 기호의 다음 런 길이를 나타내며, 기호는 1과 2 사이에서 번갈아 나타납니다. 이는 자기 생성적이고 프랙탈과 같은 수열로, 재귀 및 밀도와 같은 흥미로운 수학적 속성을 가지고 있으며 여전히 연구 중입니다.

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MontyCarloHall•1시간 전

For those not getting this immediately (I sure didn't):

              _____________
   sequence   1 2 2 1 1 2 1 2 2 1
   run lens   1 2-- 2-- 1 1 2-- 1

Read out the bottom sequence of run lengths, and be amazed that it's the same as the first 7 digits as the top sequence. Extend the bottom to continue to recapitulate the top sequence, and add terms to the top sequence accordingly to reflect the run lengths in the bottom sequence. Repeat infinitely.

AnotherGoodName•1시간 전

Can't you trivially force this to happen for any sequence?

1, 3, 3, 3, 2, 2, 2, 1, 1, 1, 4, 4,

Goes to

1, 3, 3, 3, 2... Etc.

I could extend this trivially too since the bottom sequence trails the sequence we write up top. If i wanted another '2' down the bottom whatever number i choose up top i just write twice right?

So there's nothing about this particular sequence? I can just create any such sequences trivially; Whenever you start a new count, choose a random number and repeat for a many times as needed for the trailing sequence to match the top sequence.

It seems that this particular variant is uninteresting in the broader picture right? I could write another similar one

2, 2, 1, 1, 2, 1

2, 2, 1, 1, ... etc.

I don't get the specialness here?

nwellnhof•1시간 전

There's a fascinating way to generate the Kolakoski sequence with bit fiddling: https://11011110.github.io/blog/2016/10/14/kolakoski-sequenc...

vindex10•37분 전

Is it a coincidence that it is number 2 in the OEIS?)

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