When you see this type of landscape art it's called Topiary.
Now, topiary isn't a genetic thing, plants have to be purposely shaped into those forms. And, if you look real close - they are supported by chicken wire that was shaped into the animal form with a plant growing just outside the wire.
The nice thing about topiary is that you don't need to be a vet in order to grow one. I recommend starting off by growing topiary out of a container.
Wire forms can be picked up at your local nursery. Plants best used need small leaves like: boxwood or eugenia. You can even use Ivy.