A complexity theory of generative art
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In a seminal , Philip Galanter developed a theory of generative art based on the branch of science devoted to the study of systems across all scientific disciplines, namely complexity science.
The theory is interesting for many reasons, in particular:
it gives an operational definition of generative art;
it proposes a measure of complexity in aesthetics.
Galanter defines generative art as follows:
Generative art refers to any art practice in which the artist cedes control to a system with functional autonomy that contributes to, or results in, a completed work of art. Systems may include natural language instructions, biological or chemical processes, computer programs, machines, selfâorganizing materials, mathematical operations, and other procedural inventions.
The key element in generative art is the use of an external system to which the artist cedes partial or total control. This understanding moves generative art theory into discussions focused primarily on systems, hence the proposed connection and embedding of generative art into complexity science, that is, the study of complex systems.
Another element that derives from this definition is that generative art is not a subset of computer art: a system can be and typically is a program executed on a machine; however, it might be something different, for instance a chemical reaction. Galanter quotes the Jacquard loom as a compelling example. It was Jacquard's invention (1805), introducing the notion of a stored program in the form of punched cards, that revolutionized the generative art of weaving. Later both Charles Babbage and Charles Hollerith adapted Jacquard's method of punch card programming in their efforts to invent the computer.
Computers did not pave the way for generative art; generative art helped to pave the way for computers.
Following this intuition, Galanter claims that generative art is as old as art itself. For instance, the artistic use of tiling, like the masterworks found in the Islamic world, is nothing less than the application of abstract systems for decorating specific surfaces, hence it is generative art.
Moreover, the definition of generative art says how the art is made, but makes no claims as to why the art is made that way or what its content is. In particular, the strategy employed in the definition is parametric in terms of the meaning of art itself, leaving it an open issue.
Is there a measure of complexity (and beauty) in aesthetics?
A first approach to find such a measure has been the use of Shannon entropy. Claude Shannon, an American mathematician, electrical engineer and cryptographer is known as the father of information theory. Shannon developed information entropy as a measure of the information content in a message.
To adapt the concept of entropy from information to art, one approach is to view an artwork as a message (to beholders), and try to maximize the amount of information that the message conveys. This happens to be the same as minimizing the compression rate of the message. An artwork rich of information allows low compression, while a poorly informative artwork shrinks even more when compressed.
For instance, consider the following two messages:
The first is very repetitive, and indeed can be highly compressed as , that is A repeated 40 times. The second is a random sequence of 40 symbols (in fact, an Ethereum address) and cannot be compressed. According to Shannon, the second message is much more informative than the first.
However, as much as information theory has its place in the analysis of communication channels, it does not correspond very well with our experiential sense of complexity in the world generally, or in art specifically. In particular, to the extent it equates complexity with disorder, information theory breaks down as a general model of our (aesthetic) experience. Indeed, perfect order is typically tedious and therefore not attractive, as well as chaos is incomprehensible to the human brain and therefore is equally unappetizing.
There exists a general consensus in aesthetics - the philosophical study of art, beauty, and taste - that beauty lies at the intersection of order and disorder.
Consider a performance of contemporary dance. Each dancer involved typically follows specific choreography, determined a priori by the choreographer. On the other hand, each dancer interprets the choreography according to their inclinations, history, and mood. Not infrequently, there is also room for improvisation. These elements - interpretation and improvisation - add a disorderly contribution to the choreographed, pre-given movements. It follows that every staging is the same but also subtly different from the others and t is (partially) unpredictable.
Architect Richard Padovan describes order and complexity as twin poles of the same phenomenon. Neither can exist without the other - order needs complexity to become manifest; complexity needs order to become intelligible - and aesthetic value is a measure of both. He beautifully expresses this concept with the following words:
Delight lies somewhere between boredom and confusion. If monotony makes it difficult to attend, a surfeit of novelty will overload the system and cause us to give up.
There have been attempts to devise a measure of information or complexity that is maximized when order blends with disorder. One notable example is Murray Gell-Mann's effective complexity.
Murray Gell-Mann was an American physicist who received the 1969 Nobel Prize in Physics for his work on the theory of elementary particles. In 1984 Gell-Mann was one of several co-founders of the Santa Fe Institute, a much renowned place in complexity theory. Murray Gell-Mann defines effective complexity as follows:
A measure that corresponds much better to what is usually meant by complexity in ordinary conversation, as well as in scientific discourse, refers not to the length of the most concise description of an entity, but to the length of a concise description of a set of the entity's regularities.
Thus something almost entirely random, with practically no regularities, would have effective complexity near zero. So would something completely regular, such as a bit string consisting entirely of zeroes.
Effective complexity can be high only in a region intermediate between total order and complete disorder.
To measure the effective complexity, Gell-Mann proposes to split a given system into two algorithmic terms:
a first algorithm capturing structure, and
a second algorithm capturing random deviation.
The effective complexity would then be proportional to the size of the optimally compressed first algorithm that captures structure. Galanter proposes to adopt Gell-Mann effective complexity as an aesthetic measure, partitioning generative art into:
highly ordered generative art (low complexity),
highly disordered generative art (low complexity), and
complex generative art (high complexity).
