You can if you buy seeded watermelons? Here is a modern picture of a modern watermelon with slightly less dramatic swirls. If you had bought it a few weeks earlier the swirls would be more prominent: http://sites.psu.edu/siowfa15/wp-content/uploads/sites/29639...

You can also see the swirls come out dramatically if you take a seeded watermelon and leave it in (a very cold, to avoid mold) fridge for a few weeks!

Nonsense. It isn't just a matter of ripeness, but also how many times the flower was pollinated. I got one from a friend's garden much like it last year.