Euonymus fortunei, probably the common cultivar known as 'Colorata', aka wintercreeper.

You can sever portions of the stems that have rooted from the mother plant and transplant them if you wish. This is a very tough plant and is considered invasive in some areas.

Thank you!

I tried doing that, but they never 'took'... maybe I'll try again.

Sage, That's what I did, the page I was at.. I just didn't really know if this outside plant could still be considered a house plant... if you know what I mean.

it's evergreen even in my cold climate..doesn't seem a good candidate for a houseplant to me..the prettiest houseplants are usually "tropical" plants right?..I don't think it would have a nice shape..just a super long vine..you can do better in my opinion..

I know. Would be bad for a houseplant.

And yeah I know about cold climate. I'm in Madison WI

Anything that can be evergreen in Wisconsin would be miserable and a pest magnet inside the home. If you really like it, maybe you can pot it up and just have a big pot of it near your walkway or patio outside.

I personally wouldn't do that but you were interested in keeping it so who am I to judge?