Beautiful rug. The art on wall is what you currently have? Though it’s interesting, it doesn’t complement the room. It’s too light & fluffy - the only way I can describe how it ’feels’. It doesn’t have enough color & fades into the wall. Would it work in a foyer or entry into your home? In a stairway wall? Your furniture is solid & comfy & your rug has a strong design in it. I would look for art the size of the triptych / 3 pieces you have. As for the image - that’s a personal thing. What appeals to you? Animals? Gardens? Forests? Start looking at images & see what appeals. Strong image, some solid colors from the rug in it.

I like all 3 of what @BeverlyFLADeziner shows you! They capture exactly what I was trying to convey. My personal favorite is the 1st one - the forest scene but that’s my style. Yours may be the 3rd one - the abstract.

Buy art you LOVE it will wok it is how you buy art not art to go with the rug. In fact I often buy the rug to go with the art since I only buy original art . Art is personal and needs to be something you love the rug is lovely and does not need anything to go with it. If you must then the first one from Beverly if it must "GO WITH" the rug

Visit nature and take some pics. Then have your pics blown up and framed.

Content/style is really based on your taste and keep in mind, colors need not have to match a rug unless you want that. More importantly, especially due to the short wall with lots going on, is size/placement being your first decision. See below and tape out configurations to see which feels best.

Then begin your search and I’d recommend keeping it on the lighter side. Here are some shade combinations (if you want to complement the rug) but choose what you love, especially if it’s a long term investment.

Accessories are a great way to pull a room together.

I never buy art to go with furniture or rugs!

I buy art that I love and it works in every house with any furniture.