Infinitive with “cum”

1. What does it mean to come to the infinitive?
2. What is the gerund form of come?

What does it mean to come to the infinitive?

Come + to-infinitive means that something happens or develops, perhaps outside the subject's control: At first I thought he was crazy, but I've come to appreciate his sense of humour. How did you come to be outside the wrong house?

What is the gerund form of come?

come walking come running come swimming come hopping come leaping etc.