The other way wild carrots break up their boredom is to add one red floret to the center of their inflorescences. This occurs frequently, perhaps more often than not. It seems like this is the source of the red pigment that they use to paint their outer florets. I've also seen rare green-flowered plants. I hope they continue to be rare, because I suspect this is caused by pollution.
Dutch horticulturalists found a different way to break up the boredom. We may not see their orange product in the fields, but we sure do at the market. They improved and marketed orange rooted plants as an honor to King William of Orange.