The Game of The Spider and The Bug

The Spider's Web

The above diagram depicts a spider web, where the black lines are fibers of the web, and the intersections of the fibers are called junctions.

The spider caught a bug at the center of the web, which is marked by a blue dot, and plays the following game with the bug:

• Step 1: At a junction, the bug picks a fiber (which passes through the point) to walk along.
• Step 2: The spider chooses the direction along the fiber for the bug to walk along.
• Step 3: The bug walks in that direction till he reaches the next junction.
• Step 4: If the bug touches the boundary of the web (which is marked in $\color{#20A900}{\text{green}}$), the bug is allowed to escape. Otherwise, we return to step 1 and the bug picks another fiber.

Can the bug ever manage to escape?