How to play CSS3 transitions in a loop?

CSS transitions only animate from one set of styles to another; what you're looking for is CSS animations.

You need to define the animation keyframes and apply it to the element:

@keyframes changewidth {
  from {
    width: 100px;
  }

  to {
    width: 300px;
  }
}

div {
  animation-duration: 0.1s;
  animation-name: changewidth;
  animation-iteration-count: infinite;
  animation-direction: alternate;
}

Check out the link above to figure out how to customize it to your liking, and you'll have to add browser prefixes.