I'm not sure you'd ever get purple ketchup even with purple tomatoes. Usually the purple pigments in food disappear after heating them. Do you think that'd be any different in tomatoes?
I think it depends on the particular kind of pigment. Purple berries typically stay purple when cooked, which is why blackberry pie is still purple, and eggplants stay purple also. Beets turn red, though, since the purple pigment degrades while the red one doesn't.
Not sure where purple tomatoes would fall. Some googling turns up anthocyanin as the pigment, and Wikipedia says it's water-soluble (so would leach out if the fruit is boiled and the water not retained), and changes color based on pH.
Not sure where purple tomatoes would fall. Some googling turns up anthocyanin as the pigment, and Wikipedia says it's water-soluble (so would leach out if the fruit is boiled and the water not retained), and changes color based on pH.