Computer: Telefunken TR 4

Output medium: ZUSE Graphomat Z 64

In 1967 and 1968, the artist almost exclusively used his program, “Matrix-Multiplication” generating a large set of works. Several of them are now owned by private collectors and museums world-wide.

The idea of the program is to use a simple algebraic operation, i.e. the multiplication of two matrices, to generate from a first given matrix A the sequence of its powers, A^2, A^3, A^4, … A subsequence of those – not necessarily immediately following each other – is visualized. The visualization is done by associating subintervals of [0, 1] to colors. A matrix of n x n numbers thus is transformed into a grid image of n x n colored squares.

The starting matrix A is chosen at random. It is a stochastic matrix, i.e., all its elements are between 0 and 1, and the elements in a row of the matrix add up to 1. Each power of A is then also a stochastic matrix, and the sequence of powers is approximating a state of equal rows. This mathematical theorem here becomes the source of a characteristic image behavior.