Cut a ripe tomato into quarters. Use the tip of a very sharp knife to carefully carve out all of the seeds, gel and liquid from each wedge. Deposit these parts into a glass or plastic dish, and eat the firm parts of the tomato as soon as possible after cutting it.
Spread out the tomato seeds and gel across the bottom of the dish. Set the dish out at room temperature for several days.
Stir the fermenting mixture in the morning and again at night every day for about four days. During this time the mixture will begin to smell and grow mold, but that's all part of the fermentation process.
Use a fork to carefully separate the viable seeds from the mold, pulp, gel and smallest seeds. The larger seeds will be on the bottom and will likely be darker in color than the seeds that have floated to the top. Set the good seeds down on a clean paper towel as you dig them out, then dispose of the mold and waste and rinse the dish well.
Rinse off each harvested seed, being very careful not to accidentally drop it down the drain. When all of the seeds have been rinsed, rub them back and forth in a dry paper towel to dry them out. Then spread them out on another paper towel to finish air drying for about three more days.
Put the dried seeds in a glass jar with a rubber gasket seal and seal it closed. Store the jar in a cool, dark and dry place until it is time to plant the seeds.