11. Consider an equilateral triangle with a side length of 1, denoted as $A_{1}$ (as shown in Figure 3).
Trisect each side of $A_{1}$, and construct an equilateral triangle outward on the middle segment, then remove the middle segment to obtain the figure denoted as $A_{2}$ (as shown in Figure 4); trisect each side of $A_{2}$, and repeat the above process to obtain the figure denoted as $A_{3}$ (as shown in Figure 5); trisect each side of $A_{3}$, and repeat the above process to obtain the figure denoted as $A_{4}$. Then, the perimeter of $A_{4}$ is $\qquad$