Out of thread? How to seamlessly tie a new strand of yarn

The secret sauce is named weaver's knot. Weaver's knot begins exactly like a crochet chain: You make a loop and put a u shaped loop through. Don't make the knot to tight. We want it to jump like our tatting knots in the next step.Don't leave it to loose either. It might fall apart or won't stay in place. With a little practice, you will find the best tension.

Wind your new thread on a shuttle. Make your weaver's knot at the loose end of the thread. Slip the u-shaped loop over the old thread (B.1) push it as close as possible to the last ring or chain. Pull gently at both ends of your knot (B and B.2) until the loop pulls the old thread through. At the same time keep the knot in it's position. B.1 and B.2 will be encapsulated in the next step.

Encapsulating means, we hide the ends in the double knots of the next ring or chain. Simply carry the short end with the core thread. On the picture, the thread is hold together with the shuttle. It jumps with the shuttle thread inside the knots. Should your end be too short the hold it with the shuttle, you can thread it through each knot after it jumped and before it i pulled tight. After four to five double knots, your end is fixed and can be cut off.

As I mentioned above, we need to hight two ends. (B.1 and B.2). In the picture of step 3 B.1 hides in a ring. B.2 will hide in the next ring or chain.
Of course you could hide both ends in the samy element. There are even cases, where this is the only option. I prefere to avoid this and plan a new thread far ahead. Hiding two thread at once is likely to causes tangeling. Also two hidden thread add to the volume of the knots. Your ring or chain will look very uneven.