On the infinite square grid we start with no toothpicks.
At stage 1, we place a cross, centered at the origin, formed by 2 vertical toothpicks and 2 horizontal toothpicks of length 1. At stage 2, we place 8 Dtoothpicks of length sqrt(2). At stage 3, we place 16 toothpicks of length 1. And so on.
The sequence gives the number of toothpicks and Dtoothpicks in the structure after nth stage. The first differences (A194433) give the number of toothpicks and Dtoothpicks added at nth stage.
Apparently this cellular automaton has a fractal behavior (or likefractal behavior) related to power of 2, similar to A194270 and very similar to A194434. The octagonal structure contains a large number of distinct polygonal shapes. For more information see A194270, A194440 and A194442.
