When you rub the leaves, does it have a strong, unique smell? To me, it looks like tansy.

Thank you. Yes, it does have a unique smell, sometimes strong. the leaves look more feathery than photos I've seen of ragweed . Is that only because they are young plants?

Resembles tansy, and the strong smell adds to the suspicion. It is really a rather attractive plant. When it blooms, the flowers are usually yellow and look a bit like the centers of a daisy blossom, and will be about the size of a dime or penny.

The plant is also invasive when growing in environments it likes and is considered a noxious weed in some states.

If you keep it corraled, it will make a nice plant in your landscape, but if it starts to spread you might want to remove it.

If you go to sunstarherbs.com and click on their "dye project narrative', there's a picture of a couple of flats of tansy that look like that your photos. (Tansy is a natural dye - you have to cook it with a mordant to set the color, but it generally produces a green or yellow dye.) I took a dye class many years ago at the Brooklyn Botanic Garden and learned of tansy there.

To answer your question, your patch is still pretty young (short) but it will grow taller throughout the growing season and then probably look more like some of the other pictures you've probably found.

In addition to it's dye properties, tansy is also reported to be a good pest repellant, specifically for ants. You can Google "Tansy ant" and see what comes up. All in all, I think you have a wonderful patch of tansy. Keep it!