- FASS-curve
- Finite Local Complexity
- Limitperiodic
- Polytopal Tiles
- Self-Similar Substitution
- With Decoration

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.

[hil1891]

Hilbert, D

**Ueber die stetige Abbildung einer Line auf ein Flaechenstueck**

*Mathematische Annalen*
1891,
38,
459-460,
doi.org/10.1007/BF01199431

[pau2021]

Pautze, S

**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