Holbein's "Ambassadors" (top) and the anamorphic skull in the foreground, converted using Hunt's and Nickel's formulas.

Physicists Create Funhouse Art

Look in a funhouse mirror at a carnival, and your reflection is distorted into a goofy shape. The trick works in reverse too. A curved mirror can make a distorted image appear perfectly normal. That's the idea behind anamorphic art, a technique pioneered by Renaissance painters. Although they accomplished this subterfuge by a mixture of elaborate geometry and painterly intuition, physicists have now brought anamorphic art into the computer age.

Perhaps the best known example of anamorphic art is a 1533 painting by Hans Holbein called "The Ambassadors." When viewed from an angle, a smudge at the bottom reveals itself to be a skull. A more sophisticated kind of anamorphic image, very much in vogue in the 18th and 19th centuries, becomes recognizable by laying it flat on a table and placing a cylindrical mirror in the center.

Twenty-five years ago, molecular physicist James Hunt of the University of Guelph in Ontario, Canada, read a magazine article about a touring exhibition of anamorphic art. "He kept it in the back of his mind," says his collaborator Bernie Nickel, a solid-state physicist at the same university. "When he retired a year ago, he decided he'd pursue it. One of the questions that arose naturally was: What is the math behind the images?"

The math, Hunt discovered, had all been worked out in a book by 17th century artist Jean-Francois Niceron. But it was done entirely in the geometric style of Euclid. To automate the procedure for a computer, Hunt realized the geometry needed to be translated into algebra--a fairly straightforward task, but something no one, apparently, had ever bothered to do. He and Nickel worked out the algebraic transformations, which they present in the March issue of the American Journal of Physics.

Using the formulas, even amateur programmers can write a program that will convert an ordinary picture into anamorphic art. And if you hate programming, Hunt and Nickel will do the converting for you for a small fee: See their Web site for details. The pair doesn't expect to get rich, though. "Our reason for doing this is so that other people would enjoy the fun that we've had with them," Nickel says.