I did some more thinking.

The piece can represent a lot more than seeking cures, and the mysterious nature of autism. It can symbolize the self discovery and acceptance that accompanies finding one's place in the world.

Life is a puzzle. Every individual (not only those with ASDs) is a puzzle piece. As we navigate life, we discover where we fit at our own time and place in this big puzzle. Life for an individual on the spectrum is often filled with feelings of difference and alienation, so they never seem to fit, no matter how hard they try. Once the autistic person accepts their autism, their puzzle piece fits in the world, too.