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the grid in modern painting

the grid in algorithmic art


about the grid

In modern mathematics, the two-dimensional plane is usually defined as the set of pairs of real numbers; lines and regions are subsets of this set. The plane is thus treated as an (infinitely dense) grid of locations. This mathematical point of view does not translate into a practical convention for finite computational representations, however. The mathematical correlate of any non-empty shape or line-segment is a set of uncountably many points, and the coordinates of most of these points are irrational numbers which cannot be represented in a finite way.

The conception of an image as a uniform m x n grid of colored squares is derived from the mathematical image definition in a simple, direct way. It is the discrete version of the mathematical model, which makes the image representations finite, and makes the set of image representations enumerable (if we also assume a similar discretization of the colour space). The grid therefore inherits the feel of "objectivity" of the mathematical research tradition. It is also technologically convenient, since monitors and printers are based on the same idea: m x n "pixels".

Note, however, that the grid does not inherit the mathematical properties of the mathematical image definition. Discretization is not an innocent operation. The maxim that "all directions have equal rights", which is characteristic for Euclidean space, is no longer valid: two orthogonal directions ("horizontal" and "vertical") get preferential treatment. As a result, the notions of distance and neighborhood change beyond recognition, and the Euclidean notions of translation and rotation get largely lost.

The grid does not instantiate the mathematical image conception –– it denotes it.

Remko Scha, 2003


links & references

John Elderfield: "Grids," Artforum 10 (May 1972), pp. 52-59.

Rosalind Krauss: "Grids," October 9 (Summer 1979).

Lev Manovich: The Engineering of Vision from Constructivism to Computers, Chapter I ("Visual Atomism").