Infinite Hyperbolic Scrabble Board

Again an idea based on [Voice]'s annotation to my "Infinitely Long Name For Pi".

I feel that infinite boards have been done to death, notably in 'Walking On Glass' by Iain Banks with his Open-Plan Go, so whereas this is an infinite board, it's not the usual infinite board.

A Scrabble board consists of a grid of squares with a pattern of special squares for double and triple letter and word scores. This arrangement, which I'm informed is copyrighted, is adequate for words up to fifteen letters long. There are of course a number of words which are well over that length even in English, which are however not particularly typable on the HB. However, there are also much longer strings of letters (which are arguably not words) which are mainly the names of proteins, and these could also, as [MaxwellBuchanan] has pointed out, be expanded to full organic chemistry nomenclature, which would make them a lot longer. It's probably these words, if words they be, which would form the bulk of the vocabulary required for extremely long sequences of letters, possibly accompanied by the standard organic nomenclature for genes in terms of base pairs and the like. Hence there is no shortage of words for this game, many of which have thousands of letters. On a smaller scale there are such words as "pneumono" *ultramicroscopic" "sillicovolcanoconiosis" (as one word) and the thunder words in Finnegan's Wake, whither I shall link, so it doesn't get all chemically for quite a while.

The board is infinite. Also, it's based on hyperbolic geometry in that the further from the starting point one goes, the further apart are the rows and columns, although this is gradual. The individual "squares" are also not really square-shaped, although they appear so on a small scale, because parallel lines diverge, meaning that, say, two words each of a hundred letters separated by fifty letters at their fiftieth letter might be separated by something like fifty-five or sixty letters at the start and end, assuming they both start in the same column, and the same applies to vertical words.

Moreover, it doesn't stop at triple scores. Zooming out from the starting point of the board reveals unlimited though increasingly rare higher score quadrilaterals, meaning that something like a centuple word score on a 3000-letter long "word" is possible.

The scoring of the letters is not based on the frequency of letters in English as a whole but on their frequency in the largely biochemical words on which the game is likely to be based. For instance, Y only scores one This gives humanities people an advantage on the small scale and science people an advantage on the larger one. It's also possible to prefix amino acid residue names.

Each person starts off with 343 letters (7^3) to get the game going. People work in teams from various points on the board, towards each other, conquering each others' territory by linking words, making it a bit like Go. Alliances can also be made between teams. There is scoring but an arbitrary end to the game, so it can go on forever, and of course an infinite supply of letters is available, but the limit is time or number of moves rather than a specific state of play.

There is a problem "left as an exercise to the reader". Firstly, each team starts in a location from which the words are close together, becoming increasingly widely separated further from home, but for another team a rival team's starting point is more divergent than their own. I think this can probably be exploited, or the landscape of the board can be considered as starting at peaks on a plane for each team.