The squared grid was the key to the Renaissance invention of linear perspective, a conceptual tool by which painters could represent an abstract model of the world. Persisting through the 19th century as an essential instrument of pictorial representation, the Renaissance grid was a means of objective measurement of the real, and at the same time, in its pure optical geometry, a reflection of spiritual order and human perfection—of man made in God’s image.

The grid has been a dominant motif of Modern art, used both to explore the real and what is beyond and behind that reality. With horizontal and vertical brushstrokes that mimic the gridlike weave of the canvas, Paul Cézanne fused the foreground, middleground, and background of his painted landscapes to the concrete reality of the picture plane and the rectangular boundary of its frame. Piet Mondrian utilized the linear horizontal and vertical elements of the grid to develop an entirely abstract painting embodying essential structures that underlie both a spiritual and a material world.

The historic origins and uses of the grid are tied as much to the physical reality of architecture as to the illusionist optics of painting. The modern grid also conveys the modularity of time and mechanization of the machine age—it can be seen in film frames, for example, and boxes on an assembly line—epitomized by Andy Warhol’s grid of silkscreened Mona Lisas, electric chairs, and Campbell’s soup cans. In Warhol’s works the images themselves break down into a photographic grid of dots for mechanical printing.

Marcel Duchamp, the great conceptual artist of this century, publicly gave up making art in order to devote himself to playing chess. In doing so, he recast the Renaissance grid in the form of the 64 squares of a chessboard—a fixed platform, with fixed rules, accommodating any variation of moves and an infinite array of expressive possibilities.