Collatz: halve an even number, take an odd one to (3n + 1) / 2, until 1. The snake starts as a × n and is at m whenever its whole body spells a × m.
Symbols a, b, c only: each is a pair of moves (a straight, straight; b left, right; c right, left).
real: the world is the body, bent by every symbol on the tape, and a bend can knock the snake into itself, which breaks the computation (measured: of the starts 2 to 26, these make it to 1: 2, 3, 4, 5, 6, 8, 10, 12). quiet: the same world, but the snake is a ghost to itself; every start makes it.
A snake's body, read tail to head, is a word of turns, and in Ouroboros that word is also the world. Here it is a tape. Every move writes the turn just made at the head; every move deletes the oldest turn at the tail; and the snake reads its own tail to choose what to write next.
That's a tag system: read the front symbol, delete two, append a word that depends on what you read. Tag systems can compute anything a computer can. This one computes Collatz: give it 12 and its body spells 6, 3, 5, 8, 4, 2 on the way, and it halts at 1.
The program reads the tail's bends straight off the body rather than crawling round to look; everything else is the snake's own geometry. In the real world that geometry sometimes knocks the snake off its own tape.