Research says that they are native to Europe, NW Africa and SW Asia. The purple ones in the photo look a lot like Impatiens. But the leaf tells you it's a Vinca. Vinca and Periwinkle are both common names for the Catharanthus plant which is usually a summer annual.
I haven't planted them for myself nor at any job in about 18 years! They used to get this fungus or something where about 25% of them would die pretty quickly. I couldn't afford to replace so many plants at a job. So I just stopped planting them. I stuck to Marigolds, Salvia, and Zinnias for summer color.
But I've heard that there are some new varieties of Vinca that are resistant to that die off. Some as you see in the photo still die.
Vincas used to come in just purple and white. But I love that peachy color with the dark eye and that cherry red color with the white eye. I think I'm going to try them next Spring. How do you do with Vinca?