The Peano Curve is one the earliest known FASS-curves. The original algorithm in [pea1890]
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 Peano Curve by a substitution tiling with two substitution rules and appropriate decorations.
The inflation factor
$q$ is 3 and the lines are shifted slightly away from the center of the sides to illustrate the matching rules.
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
Sur une courbe, qui remplit toute une aire plane
Mathematische Annalen 1890, 36, 157-160, doi.org/10.1007/BF01199438