It's sometimes said that the piano is an "orchestra," and one aspect of this is that we pianists can imitate other instruments on its 88 keys. Need a bass part? No problem, we'll play the low notes. Want a flute-like melody? No problem, we'll play the high notes. Want a brass section? Fine, we'll play brassy chords.
We can also imitate guitar-like textures, and fingerstyle guitar patterns are especially fun to play on piano. They let us use our 2 hands in tandem, almost like we're playing hand drums, and we can really mix up the chord tones and rhythms in inventive ways.
Here are some ideas for doing this, using the Beatles' song "Julia" to demonstrate. It's a classic acoustic fingerstyle song, and in fact, composer John Lennon learned some new fingerstyle patterns from his friend Donovan just to be able to play his own song!
Watch me play it here, and give this style a try on some songs of your own choosing. You can even use this technique on some jazz standards, as I demonstrate using "Autumn Leaves" towards the end of the video.
Enjoy, and good luck!