The Hilbert Curve is one of the earliest FASS-curves. The original algorithm in [hil1891]
bases on one substitution rule and an additional rule which describes how the substitutes have to be connected.
As briefly mentioned in [pau2021]
it is also possible to create the Hilbert Curve by a substitution tiling with two substitution rules and appropriate decorations.
The inflation factor
$q$ is 2 and the lines are shifted slightly away from the center of the sides to illustrate the matching rules.
Ueber die stetige Abbildung einer Line auf ein Flaechenstueck
Mathematische Annalen 1891, 38, 459-460, doi.org/10.1007/BF01199431
Space-Filling, Self-Similar Curves of Regular Pentagons, Heptagons and Other n-Gons
Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture 2021, 38, 157-164, bridges2021-157.pdf