An AA5 pilot reported a NMAC when a previously sighted aircraft climbed and turned into their path.

Narrative

I had a Near Mid Air Collision during the cruise portion of my flight. I was flying from ZZZ to ZZZ1 in a Grumman Traveler AA5. I am equipped with ADSB in/out and was observing traffic on my ipad; and was talking to ZZZ Approach on VFR Flight Following. I was on a northeast direction heading cruising at 5;500 ft. The controller called traffic for me crossing about 500 feet below me from right to left from the east; going westbound. I watched him; and he passed unremarkably in front of me. I then seemed to see him turning toward me and perhaps climbing in a climbing left turn; and I looked at my ipad and confirmed that was what was indeed happening. He appeared to be turning at a rate that put us on a collision course. I waited just long enough to process and make a decision. I decided to turn hard to my own left and pass belly to belly if he were to continue his turn. As we turned head to head; he leveled his wings and turned the other way; to his right. I reacted and rolled hard into a hard right turn. At that point; the conflict was resolved; I leveled my wings and watched him pass to my left. I also managed to pull AHRS data from ForeFlight to review my own maneuvering. I rolled 45 degrees to the left; and rolled directly into about 50 degrees to the right; then wings level in the course of about 10 seconds. The whole thing took about 10 seconds once I initiated evasive action.I looked at the ADSB data for this which was at XA:03; on Day 0; and we appear to be approximately .36 NM head to head with a ground speed closure rate of 219 kts. Math says that's about 5.9 seconds until that distance is closed.The controller did a great job calling this traffic and deserves recognition because it was the most mundane of traffic calls; and candidly; I've had controllers not make that call before. Today it made the difference. The controller wasn't talking to the other guy. After visiting with ZZZ Center on a tour they put on; I understood that even if I'm not going point A to B; just call up ZZZ Center; or whatever approach controller and ask for flight following... tell them what you're up to... get a code... just be able to be reached for situations that could arise. The controller did a great job of just doing his job; and it gave me a chance to see the other pilot and avoid him. I needed every bit of margin I could muster; and the controller did his job; and I did mine. See and avoid.