I had that same experience with Rothko's Number 18. Went to this Utica art museum on a field trip and while everyone else was falling over themselves to see the Real Live Jackson Pollock™ I sat in a side room taking in the orange. Had to leave before I wanted to.
I lived in a house and the staircase had a landing halfway up. The wall it faces goes to the ceiling of the floor above. and I bought a print about 2 metres of that piece to hang on that wall. I made it a habit to reflect on the idea of beauty every time I went upstairs, which is harder than it seems. Sadly I lost the habit, but it had a deep effect while it lasted. Just taking time out of your mundane daily activities to appreciate art or beauty is something to cherish.