A lot of basil smells and taste like licorice. I planted large leaf basil one year, then yanked it all out because of the licorice taste.

That looks like purple perrila to me. If it is, some people eat it, but we don't like it. There is also a colorful cultivated form, that looks a lot like coleus. And the wild form around our place is mostly green with some plants having touches of purple.

When I first viewed the photo, I thought it might be one of the red or purple basils, and many of them do have an anise or licorice scent as Carol mentioned. Then I read Dorothy's answer about purple perilla and thought she was right. Then I thought about it some more and decided it probably was perilla but that I didn't feel sure. Still, it seems more likely to be purple perilla than red/purple basil. I am linking a nice blog post that compares and contrasts the two.

Purple Basil vs. Red Perilla

I love perilla and think it is quite lovely if you have room to let it roam and reseed and spread (which it will!). However, if your growing space is very limited, you should know that it is an aggressive thug. This is the kind of plant I prefer to let grow outside the proper garden, in a space where there's native plants growing in semishade. They can just fight it out with the perilla, and whoever wins is fine with me. If you let perilla grow inside a proper garden bed, you'll be yanking out seedlings forever if you ever let it go to seed there.

I have grown one of the perillas that Dorothy mentioned that look more like a coleus. They are strikingly beautiful (but so are green perilla and red perilla). The one I grew had the best name ever: Magilla Gorilla Perilla. Whoever named it deserves a prize.

A Photo of Magilla Gorilla Perilla/Coleus is here

There's also a Magilla Vanilla Perilla. I've grown it too.

Magilla Vanilla Perilla/Coleus Image Here

Now, many years after Magilla Gorilla and Magilla Vanilla were introduced to the US marketplace, a Delaware horticultural expert tells us that they are, in fact, coleus plants and not perilla plants. See how confusing it can be with plants---sometimes it takes a horticulture professor to figure out what is what.

Botanical Accuracy: Magilla Gorilla.....

I will add then whenever I see the Magilla Gorilla and Magilla Vanilla plants in a garden center, they're usually right there beside other coleus plants, even if the growers, wholesalers and retailers continue to insist that they are perilla and not coleus. Whatever they are, they're pretty and grow well here.

I hope you enjoy your little plant, no matter what it is. At this point my vote on its identity still leans towards perilla.

Thanks for the comments everyone. I'll let it grow a little more and see if it becomes a little more clear. I'll have to agree that it looks a lot like the perilla.