In the previous section, it was suggested that for music, the definitions of conventions and style could be understood as ‘generative’ encodings. However this line of reasoning does not apply so easily to the history of visual arts. Here, style and conventions are rather related to conceptual considerations or methods of technical production, and are not so easily ‘codifiable’. In the Western 20th century fine arts, when they are defined, they instead appear as wordy ‘artists statements’. There is no ‘lattice sonics’ around which the visual arts have defined themselves. Further, images and paintings are capable to act a signifiers, representing ‘things’ in the world, whereas a ‘note’ does not inherently carry a meaning; instrumental music is not ‘about’ anything external to itself.
For these reasons, there is not the same level of codifiability in the core narratives of the history of western fine-arts, as one finds in music. However that does not mean that generative processes are not present. On the contrary, some will even contend that generative art is “as old as art itself”(Galanter, 2003). As is evidenced by the countless instances of iterative geometry and symmetry applied to textiles, drawing, sculpture, tiling, ornamentation and architecture; patterns have been present in human creative endeavours ubiquitously across cultures for millennia.
The definition of a pattern, its description, can be understood as an algorithm. Once a pattern is begun, like in a cannon, the output is ‘generated’. The artist cedes an amount of control to an abstract system. As is the case for music, wether to describe an artefact as ‘generative’, is a subjective fuzzy (non-binary) description. Rather ‘generative’ is a description of an abstract process, a mode of creation, independent of media and technological mechanisms2.
In generative design, a fundamental activity is the specification of the logic and systems that result in the patterns. Once the logic and rules are specified, these delineate the bounds of the design space within which the artists operate(Prats, Earl, Garner, & Jowers, 2006). The design space can take the form of tradition and style, the formalisms of which get passed across generations, evolve and mutate. Alternatively, artists or designers can, in a proactive and focused
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manner, be concerned with developing the systems and processes themselves, as is the case with computer art, discussed in section 2.2.4.
Patterned creation is described by Galanter as ‘highly-ordered’ generative art, the ubiquitous ancient procedures found across cultures; “The artistic use of tiling, in particular, is nothing less than the application of abstract systems to decorate specific surfaces.. the most notable examples in this regard are perhaps the masterworks found in the Islamic world”(Galanter, 2003).
Like other art forms, classical Islamic art does not exhibit a unified discourse; its styles were subject to the forces of historical changes in politics, theology and technology(Shalem, 2012). There is much uncertainty on the exact procedures by which the ancient Islamic tiling works were created, although evidence suggests that they are largely based on algorithmic and math- ematical procedures( ¨Ozdural, 2000; El-Said, El-Bouri, & Critchlow, 1993). Jowers et al. have demonstrated that they can be described in terms of ‘shape grammars’(Stiny & Gips, 1972); a formalism for the generative specification of forms, supporting the view that such works are de- signed according to a “clearly-formulated method incorporating a coherent and adaptable system of composition allowing both variation and innovation”(Jowers, Prats, EISSA, & LEE, 2010).
The tiling works of the Islamic world are remarkable in their great phenomenal visual com- plexity. However they are constructed from simple elements and forms such as squares, triangles and stars. Then through procedural sequences of translation, reflection and recombination, com- plex forms and structures emerge. The emergence resulting from these inter-combinations of the elements, exhibit properties of symmetry, scalability and a visual complexity not readily per- ceived or anticipated when contemplating the work as a set of instructions. They have a latent internal organising logic whereby a ‘specificational simplicity’(Stiny & Gips, 1972) can nonethe- less result in an emerged visual complexity.
There are numerous suggestions that this ‘emergence’ of the visual representation from the underlying structures and algorithms have theological motivations and considerations. Marks suggests that as the image is contemplated, its latent and internal logic is ‘unfolded’ by the viewer; the work embodying “a logic whereby the multiplicity of creation unfolds from the in- finite unity of God... the visual image an expression of a divine ‘logic’ that may or may not be perceptible”(Marks, 2006). Jowers et al. support this view: “the patterns support explo- ration into philosophical aspects of Islamic faith, such as the relationship between unity and multiplicity”(Jowers et al., 2010). Gocer suggest that a unifying philosophical concern of Is-
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lamic art lies in a Platonic ideal: “A philosophical explanation of the Islamic attitude toward art may therefore be derivable from the Platonic axiom that god is the paradigm of beauty, which is the cosmological principle of order and harmony; and as all created things, art, too, must reflect the divine paradigm”(Gocer, 1999). These perspectives consider Islamic art as a confluence of art, mathematics, philosophy, and religious thought.
Other cultures have also shown evidence of generative processes within theological contexts. Hindu temple architecture for instance, exhibits distinctly self-similar iteration and fractal cas- cading forms. Kirti Trivedi suggests that the Hindu temple can be understood as ‘a model of a fractal Universe’: “According to Hindu philosophy the cosmos can be visualised to be contained in a microscopic capsule, with the help of the concept of subtle element called ‘tammatras’. The whole cosmic principle replicates itself again and again in ever smaller scales”(Trivedi, 1989).
Hindu temple constructions are based on ancient texts on architectural practice called Vastu-
shastras, which describe procedural process for their design, layout and build. Trivedi points
out that they show strong parallels to approaches of computer graphics “including discretisation, fractalization, extensive use of recursion and procedures involving self-similar iteration”(Trivedi, 1989).
One such instruction reads like this -
“The layer of prahara (projection) will be above the chadya (eave of the roof). This is to be repeated again and again on the spire over the spire. A fraction of the prahara is to be constructed and again the spires are to be constructed. Each of the upper spires will be sprouted out with a measurement equal to half the size of the lower spire” - Ksirarnava, 7.113, quoted in (Trivedi, 1989).
Such a text transmits a recursive ‘program’ to be executed by masons. Initial decisions act as parameters, or seeds, that are fed into the rule sets, the resulting structure an emergent form; a kind of generative masonry. Sambit Datta further analysed such constructions and modelled the generative process in software. He was then able to algorithmically generate the self-similar fractal structures of 10th century Hindu temple architecture(Datta, 2010). He conjectures: “Con- sidering the philosophical and mathematical concepts revealed by this method of reconstruction, were ancient Hindu temple builders grappling with a method for encoding a notion of infinity through their use of geometric sequences?”(Datta, 2010)
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constructions of residential and even military buildings, the layout of towns, gardens, roads, and water works, market-places(Acharya, 1946, p. xvii).
Needless to say, procedural elements can be found in cultural artefacts in other continents. Ron Eglash, in his book ‘African Fractals - Modern Computing and Indigenous Design’(Eglash, 1999), provides a useful categorisation of cultural manifestations of mathematical processes, placing them along a spectrum from the ‘unintentional’ to ‘fully conscious’:
“At one extreme is the emergence of completely unconscious structures. Termite mounds, for example, are excellent fractals . . . we next find examples of decorative designs which, although consciously created, have no explicit knowledge attached to them. It is possible, for example, that an artist who does not know what the word ‘hexagon’ means could still draw one with great precision. This would be a conscious design, but the knowledge is strictly implicit . . . In the next step along our spectrum, people make these components explicit – they have names for the patterns they observe in shapes and numbers. Taking the intention spectrum one more step, we have rules for how these patterns can be combined”(Eglash, 1999, p. 5).
This more intentional end of the spectrum would include the examples of Islamic tilings and Hindu generative temple structures; the knowledge is externalised in a body of cultural practice passed along through tradition. These also correlate well with the trajectory of the history of mu- sic discussed in the previous section; the conventions of styles in music becoming more codified and explicit, even more so as serialism, and eventually computer based algorithmic composition practices took hold.
Eglash provides numerous instances of increasingly explicit generative practices in African cultures, with a strong prevalence for fractal structures as a ‘design theme’ that has spread across the continent: “not only in architecture, but in traditional hairstyling, textiles, and sculpture, in painting, carving, and metalwork, in religion, games, and practical craft, in quantitative tech- niques and symbolic systems, Africans have used the patterns and abstract concepts of fractal geometry”(Eglash, 1999, p. 7).
Returning to European and Western cultural practices, formal processes can often be found in folk art, ranging from fractal Celtic knots(Kaplan & Cohen, 2003), intricate geometries in Ukrainian Pyansky Easter eggs(Danko-McGhee, 1999), to the self similar abstractions of Am- mish quilts(Smucker, Shaw, & Cunningham, 2009). Perhaps the most developed practices of
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patterned design lie in the ‘fibre arts’ (knitting, crochet etc) whereby the substrate is fundamen- tally algorithmic and mathematical.
Outside the arts, the industrial revolution brought about physical generative mechanisms in the form of machinery as a replacement for hand production; manufacturing can be considered a form of generative design. One key breakthrough was the invention of the Jacquard Loom in 1805. As one of the first ‘programmable’ machines, it augmented textile machines with parame- terisation. It enabled the sequence of operations to be defined by replaceable punched cards, and in introducing the notion of a stored ‘program’, it is considered a key development in the history of computing(Fernaeus, Jonsson, & Tholander, 2012).
Within the context of Western fine-art however, generative practices would not appear until the 20th century, as the emphasis on mimetic pictorial representations faded, and the use of ab- straction would become increasingly prevalent. Spiritual concerns motivated some of the earliest abstract works, as seen in for instance in the work of Hilma af Klimt(Fant, 1986). Similarly Emma Kunz and Agnes Martin created highly patterned works of considerable geometric com- plexity within a context of a spiritual belief system. Catherine De Zegher describes the works of these three artists as analogous: “Engaging in the repetition of certain distinct geometrical shapes (square,triangle,circle etc..) marking the experiential, the spiritual and the infinite through recur- ring structures of linear patterns, the three artists believed that abstraction might be a means for achieving higher cognitive levels inextricably linked to the forces and processes of life”(af Klint, Kunz, & Martin, 2005, p. 24). Their spiritual motivations have similarities to those of classical Islamic art and Hindu temple architecture discussed earlier.
Agnes Martin would feature in the aptly named exhibition Systemic Painting at the Solomon R. Guggenheim Museum in 1966, alongside the works of artists such as Carl Andre, Peter Gourfin, and Will Insley(Alloway, 1966). Many of these works contained ordered geometric pattens created through procedural and numerical methods, and helped define the ‘minimalism’ art movement. By this time, patterns and geometric form would become increasingly common in the art galleries. Other notables including Donald Judd, Robert Smithson and Sol Lewitt, all of which used geometric and numerical systems as generative elements(J. Meyer, 2004). Further the Op-Art movement, as exemplified by Bridget Riley, also carried an emphasis on highly pat- terned visual structures, as did the works of M.C. Esher, in his geometrical “regular divisions of the plane”(Locher, Bool, & Ernst, 1992).
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The level at which these artist would externalise their processes, and how ‘implicit’ or ‘ex- plicit’ the generative procedures would vary for each style, artist and individual work. And as in music, wether to call a work an instance of ‘generative art’ is a fuzzy consideration. For some theorists such as Galanter(Galanter, 2003), and Bodens and Edmunds(Boden & Edmonds, 2009), the key consideration is that some element of artistic control is relinquished to an external system of some sort. ‘Generative art’ was not known as an explicit art movement, and rather just rep- resents a way of working, as Galanter points out - “Generative art is ideologically neutral. It is simply a way of creating art and any content considerations are up to the given artist”(Galanter, 2003).
Though chance elements had already been at work decades earlier (Mark Tobey and Jackson Pollock famous examples), previously chance occurred in the immediate rendering of the pieces (e.g. drips of paint), rather than as part of an externalised autonomous process. Sol Lewitt famously made explicit generative processes in his 1967 ‘Paragraphs on Conceptual Art’, where he stated the art should be created by formulaic rules: “The idea becomes a machine that makes the art” where “all of the planning and decisions are made beforehand and the execution is a perfunctory affair”(LeWitt, 1967). His ‘Instruction-based Art’, included chance elements as part of the generative principles, leaving decisions to be made by the interpreters of the instructions. This is a similar sentiment to some of the aleotoric works of avant-guard composers of the 50s and 60s, such as Cage, Stockhausen, Earl Brown and Morton Feldman, whereby elements of the resulting music were similarly left at the performer’s discretion.