Fill several 4-inch plastic pots with a mixture of three parts loam and one part medium-grit sand. Pour 1/4 cup of water into each pot.
Sow two artichoke seeds in each pot. Press the seeds under the soil's surface to a depth of 1/8 inch. Completely cover the seeds with soil.
Place the pots in a cold frame or indoors near a large window. Apply heat to the pots with a propagation mat set to 75 degrees Fahrenheit.
Water the artichoke seeds with 1/4 cup of water whenever the soil's surface feels dry. Pour the water into the pots carefully to avoid disturbing the seeds.
Watch for germination in 10 to 15 days. Remove the smaller of the two artichoke seedlings from each pot.
Move the artichoke seedlings into a ventilated cold frame where temperatures stay around 40 degrees Fahrenheit. Keep the seedlings in the cold frame for 10 days to chill the plants and prompt earlier flowering.
Plant the artichokes 2 to 3 feet apart from each other in a sunny bed one week after the last frost in spring. Wait until the soil reaches 60 degrees Fahrenheit to transplant the artichokes.