[get] to (thinking|wondering)

to begin considering a particular thought or idea

After the movie, she got to thinking about her own life choices.
He got to wondering if there was more to the story than what he had heard.
There are seeds in the soil, and I get to wondering how they transform into beautiful flowers.
After receiving no response, they got to thinking that something might be wrong.
There are atoms in our bodies, and I get to thinking about the complexity of life at a microscopic level.