Answered on Name That Plant. Impatiens balsamina.

We called them Touch-me-nots because the ripe pods will burst when you gently squeeze them, shooting the seeds in all directions. The pod has ribs that tighten like springs as the pod matures. They're held together precariously by all the ribs contracting against each other, but when that balance is thrown off by a squeeze cracking one of the seams, the ribs snap into a roll, and the seeds go flying.

There is a nice range of colors available: purple, like yours, red-orange, coral, pink, lavender and white. Some long-time growers have found white-spotted blooms and isolated them, so they now have seeds that fairly reliably produce spotted flowers. You can find those seeds occasionally on ebay.

There is also a beautiful "camelia-flowered" version with double blooms. It's often easier to find seeds for those than for the old-fashioned, single-flowered ones.

In any case, they are a true heirloom. I collect my seeds every year (though they have that special way to reseed themselves widely in the garden) and cherish them because I grew up with them in my mother's garden, and hers were from my grandmother (who was born in 1889), and I guess it's possible that hers came down to her through family.

Also, I agree with the previous poster. The proper name is Impatiens balsamina, and they are annuals.

HTH