Hilbert Curve Substitution Tiling

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

Info

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.

Substitution Rule

Patch

download vectorformat Hilbert Curve Substitution Tiling

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References

[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

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