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Infinite ternary word generated from the axiom 1 by the Lindenmayer system with maps 1 --> 1222131123221, 2 --> 2333212231332, and 3 --> 3111323312113.

This is a 13-automatic sequence. It can be generated by reading the lowest nonzero digit D in the base-13 expansion of n>=1: a(n)=1 for D \in {1, 5, 7, 8}, a(n)=2 for D \in {2, 3, 4, 9, 11, 12}, and a(n)=3 for D \in {6, 10}.

Corresponds to a grid-filling curve on the triangular grid as a sequence of directed edges where the letters are the directions of the third roots of unity. See the file titled "First iterate of the curve".

The corresponding sequence of turns (by 0 or +-120 degree) can be obtained from the L-system with axiom + and maps + --> +00--+0++-0-+, 0 --> +00--+0++-0-0, and - --> +00--+0++-0--.

The shape of the curve is one of the A234434(13)=15 possible shapes.

An L-system with axiom F and just one non-constant map F --> F+F0F0F-F-F+F0F+F+F-F0F-F generates the curve when 0, +, and - are interpreted as turns and F as a unit stroke in the current direction.

Three copies of the curve can be arranged to create a rep-tile that is a lattice tiling, see the files "Tile-plus" (axiom F+F+F), "Tile-minus" (Axiom F-F-F), "Tiling-plus" (self-similarity of the Tile-plus), and "Complex numeration system" (giving the generalized unit square of a numeration system with base 1 + i * sqrt(12) that reproduces the Tile-plus).