Animating a reverse walk along a worm

In each animation we walk on a spectre tile deflated a number of times, the green tiles are potentially part of a worm that has a tip that can be either internal (tip of a semi-infinite worm) or at the boundary. A pair of black spectre tiles or three tiles forming a pair of a mystic and a spectre move backwards along a worm from a boundary tip till the origin of the spectre tile (Conway signature zero). The number visible at the top-left corner displays the Conway signature of the upper black tile. From time to time the pair of black tiles rotate, showing the peculiar feature of a (bi-infinite) worm allowing the reversal of all of its tiles. The animations at depth 6 (quite lengthy) present only a partially tiled deflated spectre, in order to avoid having too many tiles in total leading to a too heavy computation time.

(non-wriggly) worms

wriggly worms