I have noticed a curious phenomenon in self-portraiture, which I hereby christen the doggy effect. It’s related to that old saw about dogs looking like their owners. What I have noticed is that artists invariably look right for their pictures. I am not claiming they resemble their output in any clear-cut or specific way. My point is that they generally look as you would expect them to look on the basis of their art. For instance, if Van Gogh had long black hair, a beaky nose and glasses, he would not suit his pictures, would he? He has to be a fiery redhead with cheekbones and stubble. Or imagine a fat and smiley Michelangelo, 6ft tall. You can’t, right? Michelangelo needs desperately to be small and intense.

But don’t trust me on this willy-nilly. Inspect the evidence for yourselves by touring the intriguing array of self-portraits that has arrived at the Dulwich Picture Gallery from, of all places, the Uffizi, in Florence. It’s a surprise arrival, because the Uffizi is one of the big guns in the museum world – the most important gallery in Italy – while the delightful Dulwich is more of a well-kept secret, an illicit pleasure. This show, with its Rembrandts and Velazquezes, is of a calibre more usually associated with the National Gallery or the Royal Academy.

It’s also a surprise because the Uffizi’s famous collection of self-portraits, the largest and oldest such collection in the world, is not generally shared with the rest of us. It hangs in a secret corridor, designed by the first art critic, Giorgio Vasari, that passes above the Ponte Vecchio and connects the Uffizi with Florence’s other great gallery, the Pitti Palace. In all my years of service in the art-critical ranks, involving so many assaults on Florence, I have never actually managed to get in there. So this show is a coup for Dulwich.

It is not, however, an undiluted pleasure. Far from it. Self-portraiture brings out various qualities in an artist, not all of them commendable. Great artists achieve great things with the genre: there’s proof enough of that here. But among art’s minnows, who naturally outnumber the giants in the 1,630 self-portraits owned by the Uffizi (fret not: only 50 have made the journey over), there is a regrettable greed for melodrama. However interesting you may find an artist, you can be sure they find themselves more interesting still. From Pietro Annigoni’s ludicrous attempt to pass himself off as Goya to Vittorio Corcos’s risible effort at capturing his own mustachioed mightiness, this show offers plenty of evidence of the minnow’s unshakable conviction of his status as a whale.

But that’s at the end of the show. At the beginning are many fine and authentic treasures. The Uffizi’s self-portrait collection dates to 1664, when Cardinal Leopold de Medici began gathering artistic like-nesses. The tradition was continued by subsequent Medici grand dukes, and when that unusually potent and possessive dynasty finally petered out, the self-portrait-hoarding was taken up by the Uffizi’s directors, and continues to this day.

The first image here takes us back to the end of the 15th century and is said to represent Filippino Lippi, the famous pupil of Botticelli, who was appreciated as much for being “courteous, affable and kind” as for his graceful and sinuous frescos. Lippi’s Caraffa chapel in Santa Maria sopra Minerva is always on my itinerary when I visit Rome. He’s as precise as Botticelli, but his work bristles with a different restlessness, as if someone has moved the dial that controls the weather in the art of the early Renaissance from breeze to wind. It’s tempting, too, to notice something coiled in the beautiful Renaissance youth recorded in the Uffizi’s self-portrait: in the way his eyes stare, in that surprising flash of teeth. There have been suggestions that the Lippi portrait is a later forgery, and I can see how there appear to be a few grams more psychology in evidence here than you might reasonably expect from a Renaissance fresco of 1485.

Lippi’s portrait is that rarest of objects, a fresco on a tile. The display ahead, however, is dominated by oil paintings, which, unlike fresco, are good at trapping elusive expressions and so comfortable in the dark. As they need to be when the doggy effect kicks in. The mysterious mannerist Francesco Primaticcio lights half of his face with flickering candles, while the other half remains hidden in the shadows. It’s a common trick. That underrated precursor of the baroque Federico Barocci uses it too, as does Bernini, taking time off from sculpture and architecture and all-round genius to try his hand, wonderfully well, at moody self-portraiture. But when it comes to lighting only half a face so the other half can skulk enigmatically in the gloom, nobody is quite as accomplished, or as determined, as Velazquez. The show’s masterpiece has the great man nonchalantly cocking his hand on his hip as his one lit eye stares down at us with the outrageous haughtiness of a Spanish monarch who has found himself in the presence of a gnat.

Rembrandt does the half-lit trick, too, but not to judge us from behind the arras. Rembrandt’s big, brown labrador eyes are filled with uncertainty: about himself, about you, about the future, about what it means to grow old. “ Suspendit picta vultum mentemque tabella”: Horace’s description of the art of painting in ancient Greece can be applied to the self-portraitist’s task, showing “both the face and the mind”. It was the portraitist’s dream in the 1st century BC, and it was the self-portraitist’s dream in Rembrandt’s studio a millennium and a half later. Put an artist in front of a mirror and the temptation for them to probe their own mental depths is impossible to resist.

The show has a marvellous beginning. Tintoretto, in his seventies, grey and bearded, looks as doomed as any of his martyrs. Carlo Dolci, that fidgety baroque genius of Florence, paints himself twice in one picture: once as a conventional artistic presence staring out at us from over his shoulder, and again as a kind of baroque Toulouse-Lautrec, dashing off a quick sketch, in the quick sketch the conventional Dolci is holding up for us to examine. (You might need to read the above description again. I promise you it makes sense. But how typical of Dolci to play mind games in the dark with his victims: us.)

While the first galleries of the show are notable for their quality, the rest are notable for their increasing craziness. The passing of the Medicis as buyers, and the arrival of a mixed bag of Uffizi directors, results in a marked drop in meaningful acquisitions as the true heroes of art are replaced by a bunch of fashionable poseurs floridly imagining their own heroism. As their names grow less familiar, so their self-presentation grows more theatrical. Most of the painters I had never heard of are Italian. Arcangelo Resani, a notorious painter of animals, I read, shows himself at work, surrounded by his livestock and, in a fine example of the doggy effect in action, bears a decent resemblance to his goat. A French nonentity, Antoine de Favray, provides the best of the unintentionally comic moments when his wrinkly little size4 head pokes out from the size16 robes of a huge Oriental philosopher.

There is much to enjoy in the parade of deluded popinjays crowding around the end of this show as they go about proving the second great truth of self-portraiture: the smaller the talent, the greater the pretension.

Artists’ Self-Portraits from the Uffizi, Dulwich Picture Gallery, SE21, until July 15

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