are the *neighbours* (in the USA: *neighbors*) of X.

We may say that a hedgehog is "one of the hedgehogs to the left" (resp.

-"right") of some other hedgehog; the meaning of this should be evident -~~-~~ it

+"right") of some other hedgehog; the meaning of this should be evident — it

is just the transitive closure of "to its left" (resp. right).

All hedgehogs share a fixed speed at which they move (when they move), and a

introduced in follower hedgehog movements, lest they get stuck.

We may want to go further, and allow the space itself to expand whenever a

-hedgehog is added to the troupe -~~-~~ so long as all the relative directions

+hedgehog is added to the troupe — so long as all the relative directions

between things are preserved, this should not affect the outcome.

(The idea for this system came to me sort of all at once when I was thinking

with appropriate modifications.

We have also not constrained the sets of faery rings and hills to be finite;

-so we could have an infinite number of them in an infinite space -~~-~~ but for

+so we could have an infinite number of them in an infinite space — but for

correspondence with a Turing machine, these should probably be restricted to

infinite sets. (Otherwise, if you have, say, an uncountable set of faery

rings, specified non-constructively, you could encode all possible