Terdragon

The terdragon is a self-similar fractal curve on the triangular grid introduced by Davis and Knuth (1970). It can be generated as a Lindenmayer system with initial string "F", replacement rule "F" -> "F+F-F", and angle .

Using coordinates on the triangular grid with basis vectors meeting at , the -coordinates of successive points begin 0, 1, 0, 1, 0, 0, , 0, , ... (OEIS A349040), and the -coordinates begin 0, 0, 1, 1, 2, 1, 2, 2, 3, ... (OEIS A349041).

After replacements, the approximant consists of equal line segments. Scaling each replacement by gives a limiting curve of Hausdorff dimension 2. Complete triangular folding versions can be extended to coverings of the plane by disjoint terdragon curves (Oger 2017).