Fourier Transformations Series (1979-1995)
The image series Fourier Transformations was created as part of Herbert W. Franke’s research into Math Art, in collaboration with physicist and programmer Horst Helbig at the German Aerospace Center DLR in Oberpfaffenhofen. The collaboration began in 1979 when Dr. Ernst Triendl, the director of the Institute of Communications Engineering at the time, invited Franke to experiment artistically with him. Triendl was interested in art himself. Franke proposed processing the equation z = x² + y² into an interference pattern using Fourier transforms. This method was significant for the image analysis of the DIBIAS (Digital Image Analysis System), which was developed at the institute. Franke later described the result, which marked the beginning of the extensive Math Art series, as Interferences. Triendl was astonished by its beauty. Franke then conceived a project to examine the aesthetic dimension of various mathematical disciplines. To this end, Triendl referred him to his colleague, Horst Helbig, who was largely responsible for developing the DIBIAS system. Over the next 15 years, the two investigated various mathematical disciplines, equations, and formulas, ranging from algebra to field equations, irrational numbers, and stochastics.The project ended when the machine and software DIBIAS that they had been working with was discontinued and DLR introduced the NASA system.
Fourier transformations are based on mathematical principles that were theoretically developed as early as the 19th century and are of great importance in communications engineering today. They are used in digital data evaluation for signal improvement and noise reduction: from satellite signals to medicine, as well as for data compression, for example for streaming TV data on the Internet or for telecommunications. With the series of Fourier transformations, Franke and Helbig used the mathematical principles of Fourier analysis for numerous artistic experiments. This results in typical ornamental structures with symmetries and symmetry breaks, which can be finely chiseled or even surface-integral. Incidentally, the math art series of letters was also realized with such Fourier transformations.
The term Math Art summarizes the results of a long series of experiments that Herbert W. Franke carried out together with the physicist and programmer Horst Helbig from 1980 onwards. It was about the use of mathematical methods, which were not developed and used for scientific purposes, but for aesthetic purposes. The main goal of the 15-year project (1980-1995) was the investigation of numerous mathematical disciplines regarding their aesthetic dimension and the visualization of complex mathematical relationships from algebraic formulas to stochastic relationships. In the course of the work, not only was the aesthetic dimension of formulas and functions explored, but a whole series of new graphic routines were also created, which were integrated into the software DIBIAS (for digital image evaluation system) as a fixed component, including representations in 2D and 3D as well as further processing with the methods of image transformation (picture processing). The heart of the Perkin-Elmer 32/52 concurrent computer was a Comtal Image Processing System and the software DIBIAS with a resolution of up to 2048 x 2048 pixels and approx. 16 million colors.