Conway's cosmological theorem on look-and-say sequences The most famous look-and-say sequence is $$1,11,21,1211,111221,\ldots$$ where the next term in the sequence corresponds to reading off the previous term, e.g. the term after $1211$ is one $1$, one $2$, two $1$, or $111221$. I was reading the wiki page on look-and-say sequences, in which it says in the section on cosmological decay: > Conway's cosmological theorem: Every sequence eventually splits ("decays") into a sequence of "atomic elements", which are finite subsequences that never again interact with their neighbors. There are 92 elements containing the digits 1, 2, and 3 only, which John Conway named after the natural chemical elements. There are also two "transuranic" elements for each digit other than 1, 2, and 3. What is this paragraph saying? I don't understand what it means by the sequences eventually splitting.

It means that for any sequence seed $a_0$, we eventually arrive at a point where $a_k$ can be written as the concatenation $b_0c_0$, such that all future $a_m, m > k$, can similarly be written as the concatenation $b_{m-k}c_{m-k}$; that is, the end of $b_i$ never mixes with the start of $c_i$, for $i \geq 0$. (The above is not intended to limit the splits to one at a time; I don't know the exact dynamics.)