Matrizenmultiplikation Nr. 1, Serie 2.5-1 (Matrix Multiplication)

Basic Information

Title: Matrizenmultiplikation Nr. 1, Serie 2.5-1 (Matrix Multiplication)
Artist(s): Frieder Nake
Date Created: 1967
Framed Dimensions: 20 x 20 in.
Unframed Dimensions: 18.75 x 18.75 in.
Inventory ID: Nake-1967-03


signed, titled, and dated on the back of the paper

artist’s name, computer identifier TR4, plotter machine identifier Z64, title, and date printed lower left

TR4 indicates the Telefunken-Rechner 4 computer used to program the plotter printer

Z64 indicates the Zuse Z64 Graphomat plotter printer used to draw the print on paper


All of the prints feature compositions of small square outlines of various different colours, which are thinly applied onto white paper. Each composition is surrounded by a thick border of blank paper. In some compositions the squares only have vertical and horizontal lines, while in others they are oriented at slanted angles. Some of the compositions totally fill the area within the border with squares, while others leave one or two blank corners or are organised into a diagonal band running from one corner to another. In most of the images some squares are printed over each other, although the extent of this varies significantly. Along the bottom of each picture is a typed text reading ‘NAKE/TR4/Z64 1967 MATRIZENMULTIPLIKATION’, followed by a numerical designation denoting the number of the ‘sheet’ and the ‘series’.

Nake made this portfolio in 1967 while living and working in Stuttgart, Germany. The images comprise three separate series. Each series was generated from a mathematical algorithm, which Nake used as the basis for several different images. According to the artist Frank Dietrich, Nake began each series by producing a square matrix on a Telefunken T4 computer and filling this with numbers. Dietrich writes that the ‘matrix was then multiplied successively by itself, and the resulting new matrices were translated into images of predetermined intervals. Each number was assigned a visual sign with a particular form and color. These signs were then placed in a raster according the values of the matrix’ (Dietrich 1986, p.161). This latter process was undertaken using a Zuse Graphomat Z64 electronic tape-punching machine. The punched tapes produced by the Graphomat Z64 were then fed into a drawing machine, which created the images. Nake commonly used random number generation in his work of this period and it is likely that his multiplication process was partly automated. The portfolio was published by the artist Hansjörg Mayer in an edition of forty. Twenty-six of these are lettered from a to z and signed by the artist. This portfolio can also be found as letter “p” in the collection of the Tate.

This is one of many works of computer or algorithmic art that Nake made between 1963 and 1971. All of these include abstract images produced using a computer, a tape machine and a drawing machine. Other artists such as A. Michael Noll and George Nees were also working in similar ways during this period. The title of this portfolio refers to Nake’s practice of producing numerical matrices and then programming a computer to multiply the numbers various times. The title therefore draws the viewer’s attention away from the finished picture and towards Nake’s computational process. This emphasis is perhaps explained by his statement in 2010 that ‘every individual piece of algorithmic art is no more than only one instance of the potentially infinitely many from the class of works defined by the algorithm. The tragedy is that the algorithm itself does not often show visual qualities. Its qualities are the potential to generate visual works. But each of its visual products is a shadow only of the algorithm’ (Nake 2010, p.56).

The art historian Grant D. Taylor has argued that Nake’s computer-based methods ‘break with the traditional process of building an image from visual structures, because the input data is merely computing operands’ (Grant D. Taylor, When the Machine Made Art, London 2014, p.78). Nake has gone further, arguing that in computer art, ‘The individual human subject simply did not exist anymore, once he or she had set the boundary conditions for the image to be computed’. Nonetheless, in the same text he also acknowledged that his computer art remained somewhat ‘traditional’, since it ‘resulted in paper work to be put up on the walls of a gallery’ (Nake 2010, p.62).

Further reading
Frieder Nake, ‘Notes on the Programming of Computer Graphics’, in Jasia Reichardt (ed.), Cybernetic Serendipity: The Computer and the ArtsStudio International Special Issue, London 1968, pp.77–8.
Frank Dietrich, ‘Visual Intelligence: The First Decade of Computer Art (1965–1975)’, Leonardo, vol.19, no.2, 1986, pp.159–69.
Frieder Nake, ‘Paragraphs on Computer Art, Past and Present’, Cat 2010: Ideas before Their Time: Connecting the Past and Present in Computer Art, Swinton 2010, pp.55–63.


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