>and to re-grow when cut back.

it doesn't actually do that, you are just experiencing hair life-cycle.

hair grows out to x length, and then stays that long for however long (head hair is ~2 years, body hair can be as short as two weeks), then the follicle "dies", the hair falls off the follicle, and then the follicle regrows itself and does it all again. If you cut a hair in half it will be half as long for the rest of the life cycle - this is why regrowing cut head hair takes 2+ years to get to full length (although head hair is a bit special because it doesn't have a cap length), but e.g. chest or leg hair can recover in a month or two, and will APPEAR to recover even faster, because half your hair was at the end of the its cycle when it got shaved.