The Game of The Spider and The Bug

Logic Level 3

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 $\color{green}{\text{green}}$ ), 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?

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