Second photo looks like a chrysanthemum

I was thinking mugwort, Artemisia vulgaris, for the second. Check the leaf reverse to see if it is silver or green . Silver = mugwort.

http://coffeeforroses.com/i-hate-artemisia-vulgaris/

Yes, the first is an artemisia also.

doesnt the fact that they are taking over the area ... give you the answer you want ... in terms of friend or for.. i mean ...

IDing them.. of course is knowledge .. and knowledge is good ... but heck.. they are still taking over ...

ken

It's so weird since I never planted either of them so I don't know how they got there, unless birds deposited seed there.

sweet_Betsy, I thought the same thing, that's why I left them in last year. But they never flowered. They will get pulled and disposed of because they look weedy to me anyway. I like the silver colored plant though and might pot some of that up.

Ken, they are obviously foes if they are taking over an area. But, since I plan on redoing this whole area anyway, I will get rid of any aggressive plants. Besides, If they are ornamental, I can dig them up and pot them. I know plenty of people who grow mint and other aggressive plants in pots. There are plenty of plants I grow that I love that can be absolute thugs, but since I love them I just deal with them aggressively and pull away. I love Rudbekia trilobal, Feverfew, Lysmachia (Creeping Jenny) but they spread from one end of my garden to the other. But, since the seedlings or creeping are easy to spot and pull when I am doing my normal weeding anyway, I don't mind the extra work. I feel the same way about wild Marjoram and Lauren's Grape Poppy too. For me, some plants are just worth the extra effort. Anyway, I don't have a formal garden. It's more like a cottage garden a la Tasha Tudor. My Folk Victorian house wouldn't look as well with a more formal garden.

Thank you everyone for all your expertise on the subject. You've all been a great help.

Mugwort is a terrible thug. You'll have to keep after it for several years to get rid of it all.

callirhoe123, which one? The green or silver plant?

Both are mugworts and both can spread aggressively. The green maybe faster than the gray/silver one.

The second one is Artemisia vulgaris, commonly known as Mugwort, a wild plant which qualifies as a weed in most gardeners' opinions. The first is Artemisia ludoviciana which many people consider a perfectly garden-worthy subject. There are named selections.

The silver one is native to continental north America. The green one is native in Alaska, but not the continental U.S. I do like the silver one better also.

The green one.