I must generate at least upto level 16 and I hope that you will come up with some hint to get around this issue. I tried to step through GDB and I found that the program crashes at
current = next;
A better way to formulate the algorithm is requested from the forum.
Do you realize how big your string is getting? Remember you're algorithm has exponential growth. You're going to run out of space for your string well before you reach generation 16.
Remember a string, or any container can only hold a finite amount of data. The amount is limited by your operating system, processor type, and several other limits.
If you really want to generate a pattern this big I suggest you think about using some files.