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.
Finite Local Complexity Polytopal Tiles Self Similar Substitution With Decoration Limitperiodic FASS_curve