I don't have an animation, but it is so simple.
Air goes in from the tank to the inline reg. The inline brings the pressure to a reasonable level. Now, the air goes to the LPR and the valve. The LPR makes the air pressure even more reasonable, and sends it on to the solenoid. When you pull the trigger, the solenoid switches the air path. Without pulling the trigger, the air always goes to the front of the ram sleeve. That pushes the ram back. If you pull the trigger, the solenoid switches, and sends the air to the back of the ram sleeve. The ram sleeve is that part that is in the lower part of the receiver body, right above the grip frame. When the air pushes from the back of the ram sleeve, the ram slides forward. It smacks the valve and lets air go up into the bolt. Since the bolt is attached to the ram, it has moved forward also, and pushed a ball into the end of the barrel. Now, that air which didn't go through the LPR goes up through the bolt and pushes the ball out the barrel really fast. Then, after an amount of time determined by the programming of the circuit board, the solenoid again routes the air to the front of the ram sleeve.
So simple, it shouldn't work half as well as it does.