An idea from Jean Hoffmann.
In this cellular automaton a Vtoothpick is formed by 2 toothpicks of length 1 that share a vertex and the angle between both toothpicks is 60 degrees.
On the infinite triangular grid we start with no Vtoothpick, so a(0) = 0.
At stage 1 we place a Vtoothpick upside down, so a(1) = 1.
At every stage the Vtoothpicks of the new generation must be connected to the structure by touching with their middle vertex the free ends of the Vtoothpicks of the previous generation following a special rule:
The new Vtoothpicks must be placed between the imaginary straight line containing the two extreme ends of the Vtoothpick of the previous generation and the imaginary straight line that contains the middle vertex of that Vtoothpick and that it is parallel to the aforementioned straight line.
A355311(n) gives the number of Vtoothpicks added to the structure at the nth stage.
2*a(n) is the total number of toothpicks of length 1 in the structure after nth stage.
This cellular automaton is a companion of the Ytoothpick cellular automaton of A160120 in the sense that both essentially grow as an equilateral triangle.
This cellular automaton is slightly less symmetrical than Ytoothpick cellular automaton because its structure has a "backbone" formed by concave hexagons from the center of the triangle to one of its vertices.
The behavior could be very close to A160120 and similar to A153006 (see the graph).
After 18 stages we can see in the structure the following polygons:
 Equilateral triangles of perimeter 3.
 Equilateral triangles of perimeter 6 that contain 4 triangular cells.
 Concave hexagons of perimeter 8 that contain 6 triangular cells.
 Concave dodecagons (or concave 12gons) of perimeter 18 that contain 22 triangular cells.
