Minimial generative principles for large
scale drawings: an experimental
approach and its results.

Prof H.E. Dehlinger, PhD
Department of Product Design, University of Kassel
Director of the Institute Design-Kunst-Computer
Universityof Kassel, Germany.

e-mail: <>

The line as an element or linear structures as such can be observed in
many circumstances and in many places of our daily lifeīs. Lines have
poly semantic characteristics and the word line is denoting much more
than a long thin mark made by a pencil. The concept of a line is a very
rich concept, and it seems, each epoch of art is developing its own
codes for lines to deposit its world views within them. The emergence of
generative approaches is characteristic of our epoch, and it is lines as
elements of drawings generated by algorithms, executed on machines, and
drawn with a pen equipped plotter on which this work is based.

1. The Generative Environment
Algorithmic procedures will be used to trigger the generation of a
drawing or any part of it. This approach calls for some explicit
definitions to take care of the generative environment. As we will see,
these definitions are rather restrictive, and they will most likely be
questioned by any other artist. It is difficult if not impossible to
formulate minimal sets of procedural rules for art without receding to
the intentions of the artist [1]. Or, stated in other terms: By defining
a distinct intentional base, an artist may choose to formulate a minimal
set of such rules - not once and forever, but for the sake of pursuing
the task at hand. Since the intentional base is very personal, almost a
personal ideology, it follows, that a multitude of generative
environments will exist, and each one can be justified by the intentions
of an artist. What I call the intentional base may also be thought of as
the formulation of a concept for, or the idea or program behind an art
production. Giving it a name like constructivism, minimalism, art from
art etc., is a semi magic act trying to ban the unknown, to conquer it
and rule over it. And, the power and strength of the generative rules
will have a determining impact on the results. In generative art, the
rules on how to instrumentalise the intentional base must be laid down
beforehand with considerable precision. This holds for "generativism" as
well as for the more traditional approaches. It is here, where the
notion of a rule set, which is valid in a vague and fussy sense for many
traditional art productions as well, takes a sharp turn to follow the
strict definitions of computer science. An artist, working by hand on a
drawing may act according to a preconceived rule set and "make short and
powerful strokes" with the hand, or "go to and fro in the direction of
the developing line", or "draw in small, circling movements" [xx]. But
it takes a number of further efforts to cast the logic of such actions
into the strict algorithmic format of computer programs on which
generative art is relying, and which are defining the generative environment.

Fig.1 GA 99 Milano: Experiment No. 30c

2. Minimal Generative Procedures
The experiments I want to discuss rely on a minimal set of rules an
these are defined by:
(1) An area D in which a drawing is allowed to evolve.
(2) An area P in which a set of starting points is located.
(3) Lines as polygons p (i, j), with i, j denoting the i-th line in P
The area D is the drawing area and it may be of any geometric shape.
>From the point set located in P, lines will start to develop and they
emerge and become visible as soon as they enter D and as long as they
stay within D. The bounded area P may be anywhere on the plane: Outside
of D, partially outside of D or within D. Like D, P can be of any shape.
For lines, only polygons are permitted. Note, that his is a very narrow
definition for a line. The restriction to use polygonal lines only and
as the sole elements of a drawing is also unusual with respect to the
bulk of existing drawings. It has obvious advantages (e.g. simple to
calculate) and obvious disadvantages (e.g. many drawings are conceivable
for which polygonal lines are not well suited). The strongest argument
for such a constraining definition of lines is again founded in the
intentional base of the artist. It can be a deliberate choice to adopt a
brittle material despite (or because of) its otherwise and quite obvious
shortcomings. In all of my drawings I have chosen to use polygonal lines
as the only type of line. It is a challenge to use them in a generative
approach because this type of line is so far removed from any line drawn
by the hand of an artist.

Fig.2 GA 99 Milano: Experiment No.34c Fig.3 GA 99 Milano:
Experiment No. 33c

With the above definition, we can start to generate drawings along the
following generalized minimal procedure:
* generate a drawing area D; cast a set of points into area P; generate
lines from P into D.

This set of rules is an example of a minimal generative procedure
because it is reduced to essential entities. It follows the advice of
Occam [2], stated in his famous principle. Omitting any one of the three
will prevent a result. Because it is concise and simple, it is a useful
basic building block for a generative approach. It allows for a rich
generation of variety within a large domain of possible objects. It can
be applied with repetition and it can be expanded to unlock other
domains of variety. We can imagine a universe of generated drawings
using polygonal lines only. And it seems to be a very rich universe. The
drawings in the universe of polygons are unique. They are very different
from drawings located in other imaginary universes. The straight
segments of a polygon, the variations in length, direction, spread; the
position and relation of one polygon to others; the crossing, joining,
touching, departing, converting etc. of a large population of polygons
in a drawing make up for a characteristic calligraphic quality and a
unique expressive momentum. This quality is further enhanced by plotting
the drawing with a pen or pencil instead of printing it . Two lines
crossing each other drawn with a pen produce a type of visual depth
which is hardly achieved with the binary logic of a black and white
When we observe the work of other artists working along similar lines of
an algorithmic generation of artwork, we find that many of them have
defined their own minimal set of rules. Verostko and Steller are two of
them, but there are many others.
Verostko [3] for example frequently uses a continuous, function driven
line which is characteristic for his work. It is based on a "very lean
code" [4] which may be considered a minimal set of generative rules
in itīs own right.
Fig.4 GA 99 Milano: Experiment No.3c Fig.5 GA 99 Milano:
Experiment No. 32

Steller [5] uses fractions of Lissajous-Figures which are produced by
oscillations. The pictures are highly magnified "break-outs" of a
displayed function, and the gems form the production are fished out by
inspection. Both artist have shown how rich the produced variety can be
by exploiting a generative environment based on a minimal set of rules.

3. Some Experimental Results
With the rule set discussed above, some experiments have been carried
out, which will be explained in the following remarks.
Figure 1 is generated from two different P-areas which are both located
outside the drawing area D. The lines become visible as soon as they
enter D and as long as they stay within D.
Figure 2 and 3 show sections of drawings which utilize a number of
irregular shaped D-areas. The P-areas are all located outside of
D-areas. For some Dīs, there is more than one P-area.
Figure 4 is generated from a P-area outside of D, and there is only one
D-area and one P-area. Parts of figure 5 show P-areas within D and the
generated lines do not touch the borders of D.
Fig.6 GA 99 Milano: Experiment No. 31m2

Figure 6 is generated from a repetition of three identical P-areas
located outside D. They are slightly offset with respect to each other.
Figure 7 and figure 8 show drawings which resulted from following the
approach used in figures 2 and 3.
Expanding the minimal set of rules is not difficult and it may follow
various directions. Some candidates for such expansions are: (1)
changing the character of a line, when it is crossing into another area.
A line may then for example grow thicker or thinner, or disappear, or
change into a dotted line, or into broken line and so on; (2) allow for
other line types; (3) introduce areas D in which all lines will disappear.
Fig.7 GA 99 Milano: Experiment No. 28

4. Concluding Remarks
The experiments I am presenting here should not be seen as attempts to
investigate the plotted line as a new mechanism of expression. Even if
there are connecting links to the classical heritage of hand drawings,
the goal of this experiments is to point out and reveal the unique
features of drawings which own their existence to a generative, machine
oriented approach. I regard the universe of such drawings as an
extension of the sphere of classical drawings, and it adds an entirely
new field of exploration to this sphere.
Fig.8 Stein, (Ausschnitt)


[1] Soddu, C., Generative Art. Proceedings of the 1998 Milan First
International Conference Generative Art ī98. Generative Design Lab,
Milan Polytechnic, Milan 1998.

[2] William of Ockham, ca. 1285 - 1349;
14th century logician and Franciscan friar.
Occam`s (or Ockham`s) Razor is a philosophical principle attributed to
him, stating:
Entia non sunt multiplicanda praeter necessitatem"

[2] Dehlinger, H.E., A Genetic Approach to the Generation of Line
Drawings; Proceedings of the AISBī99 Symposium on Creative Evolutionary
Systems, Edinburgh College of Art and Division of Informatics,
University of Edinburgh, 1999

[3] Verostko, Roman, Artist, Professor Emeritus, Minneapolis College of
Art and Design.

[4] cited from memory of a personal conversation

[5] Steller, Erwin; Aspekte Konstruktiver Kunst XXI,
E-Werk Hallen für Kunst, Freiburg, 1999.