This is a cellular automaton of forking paths to 135 degrees which uses elements of three sizes: toothpicks of length 1, Dtoothpicks of length 2^(1/2) and Dtoothpicks of length 2^(1/2)/2. Toothpicks are placed in horizontal or vertical direction. Dtoothpicks are placed in diagonal direction. Toothpicks and Dtoothpicks are connected by their endpoints.
On the infinite square grid we start with no elements.
At stage 1, place a single Dtoothpick on the paper, in diagonal direction.
The rule for adding new elements is as follows. Each exposed endpoint of the elements of the old generation must be touched by the two endpoints of two elements of the new generation such that the angle between the old element and each new element is equal to 135 degrees. Intersections and overlapping are prohibited.
This toothpick structure is very similar to A194270, but here there are no toothpicks endpoints that remain exposed forever.
