Answer: What you've discovered isn't all that unusual, and it isn't limited to just one variety of tomato. Tomato seeds are encased in a gelatanous substance that inhibits seed sprouting. (So new plants won't sprout right away and compete with the parent plant.) When tomatoes are barely overripe the substance begins to break down and the process of fermentation begins. Couple this with the warmth from the sun and you have a perfect incubator.
To this scenario add the fact that the last thing a plant does before it dies is produce seed (to continue the species). So, your tomato plants are producing very vigorous and viable seeds, and the environmental conditions are perfect for the germination of these seeds. Homegrown tomatoes aren't the only fruits to contain sprouting seeds - I've discovered the same thing in store-bought tomatoes.
The fruits are safe to eat, but I always remove any sprouts I find.
Bush Early Girl and Super Tasty are both resistant to alternaria. Early Pick, Early Girl and Celebrity are all resistant to fusarium and alternaria. You'll probably have good luck with Brandywine in your garden, as well.
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