Here is a small sample of this worked up.
Use 20 gauge rings.

Step 1. Start with 2 closed 4mm rings

Step 2. Add 1 6mm ring.

Step 3. Add another 6mm ring, but pass through both 4mm rings and make sure it stays in front of your first ring.

Step 4. Add another 6mm ring to the other 4mm ring. Make sure this one stays in back of the center (purple) ring.

Step 5. Now add a 4mm ring, passing through both the center 6mm ring and the ring behind it.

Step 6. Add the other 4mm ring, passing through the center 6mm and the one behind it.

Repeat from step 2 until you have the desired length. Another cool thing to do, that would look nice as a bracelet or necklace, is after each complete bubble, make a spiral chain and join the bubbles together. 

This is what the next link looks like.