texaskitty111 said:My question is - if I grow a tomato that looks exactly like an Arkansas traveler picture, and I really love the taste, would it be safe to assume the seeds will grow an Arkansas traveler?
You can't assume that it is an Arkansas Traveler Tomato unless you grew it from seeds that were Arkansas Traveler or you purchased a plant labeled Arkansas Traveler. And even that is not a guarantee.
There are thousands of tomatoes and it would be impossible to identify one from a picture or even taste.
Like Rick said, you can bag the fruit to save seeds and you will most likely get the same fruit as the parent plant produced.