In 1969, I published my first visual artist book "Artificiata" with Edition Agentzia in Paris.1 It was a visual-poetry book and also my last art work drawn by hand. At the time, I proposed to create a second Artificiata based on algorithms and calculated and drawn by computer.
Since my visual research around 2012 developed a strong relationship to visual-music in a music score-like flow, similar to Artificiata of 1969, I decided to call this work Artificiata II and at the same time created a visual-book with the same name. I published Artificiata II in 2014 with OEI Editor in Stockholm 2, exactly as I had imagined it 44 years earlier.
In this work, a "diagonal-path" from a hypercube, randomly chosen between 11 and 15 dimensions, is drawn. A diagonal-path is a multiple-segmented line where each change of direction indicates the passage through a single dimension (diagonal paths were introduced into my work in "Dimensions I" in 1978). 3
Horizontal lines are attached to the line at each change of dimension, i.e. the horizontal lines are drawn through the y-value of each vertex of the diagonal path when it is projected into 2-D. The spaces between the horizontal lines on either side (left/right) of the diagonal-path are filled with distinct sets of randomly chosen colors. The same procedure also calculates lines and colors in the vertical direction through the x-value of each vertex. The vertical lines are not drawn, but the resulting color sets are retained. This procedure creates four color sets from which three are randomly chosen to construct the resulting image. By overlaying the color sets successively, unpredictable constellations appear.
The color spaces and horizontal lines move with the structure when the diagonal path (white line) is in slow motion (rotating in hyper-dimensional space and then projected into 2-D), and can be observed in my real-time computer animation works.
The animation algorithm of P1622 contains random variations of speed and suites of stills, adding a musical rhythm to this work. The works on canvas P1611 are therefore instants from this animation. The algorithm is described above. This part of Artificiata II was published in a fold-out catalog in 2013. 4
Projections and Dimensions:
The animation P1660 shows all the 2-D projections of a randomly chosen n-dimensional diagonal-path between 2-D and 13-D in a cyclic mode. Similar to the rules in 12-tone music, each dimension has to be selected once before the same dimension can appear again.
Program P1650 shows on paper a complete set of all the 2-D projections of a n-dimensional diagonal-path between 2-D and 13-D. The algorithm of each individual projection in an image is described above.
Parity - Fracturing n-dimensional diagonal paths:
This work series P1682 shows the fracturing of a diagonal-path into even and odd numbered lines. The algorithm also refers to the procedure described above: relating the attachment of a diagonal-path to its horizontal lines.
Traces - Capturing the history of n-dimensional rotations:
In Program P2200, the thick white line shows a rotated n-dimensional diagonal-path projected into 2-D and the color lines show the history of that movement restricted to the 2-D rectangular space. The algorithm also refers to the procedure described above: relating the attachment of a diagonal-path to its horizontal lines.
The animation P2210 shows instances of this program.
1) - Artificiata I, preface by Pierre Barbaud, Edition Agentzia Paris, 1969
2) - Artificiata II, afterword by Margit Rosen, OEI Editor Stockholm, 2014
3) - Exhibition Catalog "Dimensions I" (4-dimensional hypercube), Galerie Mueller-Roth, Stuttgart, 1979
4) - Exhibition fold-out Catalog, "Artificiata II" Galerie Mueller-Roth Stuttgart, Galerie [DAM] Berlin, 2013