The original Heighway Dragon Curve as described in [gar1967]
, can be derived by a substitution tiling with one substitution rule and appropriate decoration.
However, it is not a FASS-curve because it is not self avoiding.
With the results in [pau2021]
it is possible to derive a substitution tiling which generates a Heighway Dragon FASS-Curve without disturbing self similarity.
In detail the decoration on the proto tile is shifted away from the corners in different ways. As a consequence of the combinatorics the number of substitution rules increases to four.
Furthermore the vertices of the FASS-curve are not preserved by the substitution rules.
The inflation factor
Scientific American 1967, Volume 216, Issue 3, 124-127, 10.1038/scientificamerican0367-124
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