``Aber die Erkenntnis ist mein, dass es in der ganzen Welt, in allen Welten, nichts Ungesetzliches, nichts Zufälliges, nichts ohne Form und Rhythmus gibt noch geben kann. Warum dann gerade in der Kunst? Soll diese nicht dann, indem sie des Menschen schöpferischen Willen offenbart, gerade voll Form, voll Gesetz und Geist sein?''English translation (free translation by the author -- subtleties in the original text source may be lost):

``But the insight is mine, that in the whole world, in all worlds, nothing unlawful, nothing random, nothing without form and rhythm exists nor can exist. Why then in the arts? Shouldn't the arts, by exhibiting man's creative will, be filled with form, law and spirit?'' [12]

The ancient Greeks, Leonardo da Vinci, Albrecht Dürer,
LeCorbusier and many others devised formal rules
to draw things.
Most rules
are based on simple proportions--for example, ``The distance
between the eyes should equal the eye-width" (origin unknown), and
``The ratio of the distance from toes to navel and the distance
from toes to top of the head should equal the harmonic proportion"
(LeCorbusier). (The harmonic proportion is obtained when a
straight line of length *a* is divided into two
segments of lenghts *b* and *c*, such that
a/b = b/c. One solution is
b = a (sqrt(5) - 1)/2.

I do not claim to be the first to present examples of low-complexity art, however. Certain representations of artistically interesting and aesthetically pleasing representations of fractal objects may be regarded as works of low-complexity art, such as pictures of hills, coastlines, etc. [13]. This is because they are based on relatively short and understandable algorithmic descriptions. Also, certain data-compression methods can be used to generate patterns that can be regarded as works of low-complexity art [14]. Similar statements could be made about certain other simplifying computer models for representing objects [15]. Also, many graphic designers consciously or unconsciously use their tools to come up with algorithmically simple designs.

Apparently, however, nobody so far has identified low-complexity art and low-complexity design as such in its most general form. An aim of this paper is to make explicit the nature of low-complexity art and low-complexity design--the creation of understandable works of art (or designs) with low Kolmogorov complexity. This also provides a framework for the categorization of previous work.

Finally, it should be mentioned that there have been attempts to use classic information theory [16] to formalize what is aesthetically pleasing [17]. Another contribution of this paper is to offer an alternative approach based on algorithmic information theory.

Back to Theory of Beauty page

Back to Algorithmic Information page