Gangs of Vermeer fans are flocking to the US's east coast, where 40% of all his work is currently on display. I salute them

Vermeer, that genius of quiet intensity, has some very intense fans. According to the New York Times, superfans are flocking to America's eastern seaboard, where an exhibition at the Frick, added to his excellent presence in permanent collections in Washington and New York and a loan at the Philadelphia Museum of Art, means that nearly 40% of his known works can currently be seen in the same region.

The Times reports that Vermeer superfans, whom it compares to Wagner enthusiasts, are travelling to America specifically to see this constellation of his works. And why wouldn't they?

Money apart, it's well worth dedicating yourself to a great artist such as Vermeer. Why should this be thought unusual? People lavish time, funds and effort on cultural activities that are far less rewarding, from football to concerts by ageing rock stars. Vermeer is a profoundly rich and complex artist whose works mirror the living world. He has an enigma at his heart and there are only a limited number of paintings by him extant – so you can strive to see them all.

I may even have done so. I know I've seen his paintings in New York, Washington, the Hague, Amsterdam, Vienna, Paris and London. That can't leave too many I have not seen. And I wouldn't even say I was a Vermeer superfan. What I am is a Leonardo da Vinci nut. At the height of my obsession with him, I travelled to New York and Paris to see exhibitions of his drawings, repeatedly took the train to France just to see his paintings in the Louvre, talked my way into the Royal Library at Windsor to go through boxes of his notes, and made pilgrimage upon pilgrimage to Florence.

The lovely thing about Leonardo is that you don't have to spend this much time and money to find him rewarding. His art reproduces easily and his notebooks can be read anywhere in paperback. After blowing all my money on the travels described above, I just sat down with some picture books and found Leonardo even more mesmerising.

But I think it is worth being a slave to art. Some artists just get their hooks in you and ask you to find out more about them. You feel utterly compelled to track down their masterpieces – reproductions will not do.

As well as doting on Leonardo, I confess to being a Michelangelo and Caravaggio groupie. I have made it my business to see the almost complete works of Michelangelo – his Madonna in Bruges is the only one of his sculptures I have still not seen face to face – and I have taken a trip in search of every painting by Caravaggio.

It doesn't pass, this addiction. I've seen all of Caravaggio's paintings in Italy but last summer, in Rome, it suddenly hit me that I had to see his picture of St Peter in Santa Maria del Popolo, immediately, and I dragged my family across the city, way off course, in the hot afternoon. We'd already seen three Caravaggios that day – why did I need another? I just did.

Great art is deeply compelling. It makes groupies of us if we let it. And it is truly worth the effort, so why not? I don't think the people making a pilgrimage to the Frick's Vermeer exhibition are eccentrics. I think they are true art lovers.