## Heighway Dragon FASS-Curve Substitution Tiling

### Info

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 $q$ is $\sqrt{2}$.