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feasible values. Such requirements defined a set of up to 2
r
constraints. In addition,
the aesthetic measure that Gunzenhäuser had defined as an information-theoretic
analogue to Birkhoff's famous but questionable measure of “order in complexity”
(Birkhoff
1931
) could be required to take on a maximum or minimum value, rela-
tive to the constraints mentioned before. Requesting a maximum to be the goal of
construction put trust on the formal definition of aesthetic measure actually yielding
a good or even beautiful solution. Requesting a minimum, to the contrary, did not
really trust the formalism.
With such a statement of the problem, we are right into mathematics. The prob-
lem turns out to be a non-linear optimisation problem. If a solution is possible, it had
to be a discrete probability distribution. This distribution represents all images sat-
isfying the constraints. it was called “the statistical pre-selector,” since it was based
only on a statistical view of the image. In a second step, a topological pre-selector
took the sign schema of the previous step and created the image as a hierarchical
structure of colour distribution, according to the probabilities determined before.
The type of structure used for this construction of the image was, in computer
science, later called a
quadtree
. A quadtree divides an image into four quadrants of
equal size. The generative algorithm distributes the probabilities of the entire image
into the four smaller quadrants such that the sum total remains the same. With each
quadrant, the procedure is repeated recursively, until a quadrant is covered by one
colour only, or its size has reached a minimal length.
Generative Aesthetics I
thus bravely started from specifying quantitative criteria
that an image was to satisfy. Once the discrete probability distribution was deter-
mined as a solution to the set of criteria, an interesting process of many degrees
of freedom started to distribute the probabilities into smaller and smaller local ar-
eas of the image but such that the global condition was always satisfied. Aesthetics
happened generatively and objectively, by running an automaton.
The program was realised in the programming language PL/I with some support
from Fortran routines. Its output was trivial but fast. I was working on this project
in Toronto in 1968/69. Since no colour plotter was available, I used the line printer
as output device. The program's output was a list of measures from information
aesthetics plus a coded printout of the generated image. I used printer symbols to
encode the colours that were to be used for the image.
This generative process was very fast, which allowed me to run a whole series
of experiments. These experiments may constitute the only ones ever carried out
in the spirit of generative aesthetics based on the Stuttgart school of information
aesthetics. The program was intended to become the base for empirical research
into generative aesthetics. Regrettably, this was not realised.
With the help of a group of young artists, I realised by hand only two of the
printouts. From a printer's shop we got a set of small pieces of coloured cardboard.
They were glued to a panel of size 128
128 cm. One of those panels has been
lost (Fig.
3.8
). The other one is in the collection Etzold at Museum Abteiberg in
Mönchengladbach, Germany.
Besides the experience of solving a non-trivial problem in information aesthetics
by a program that required heuristics to work, I did this project more like a scientist
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