Generative Art in Visionary Variations
(at University of Colorado, Boulder)
Generative Design Lab
Politecnico di Milano University
For gaining a visionary aesthetical work we need a lot of different tools. Henry Focillon said in "Aesthetics of Visionaries" that Visionary looks at an achievable future and designs original tools for constructing his own visions using endless variations.
My approach to generative design uses mathematics, algorithmic complex systems, non-Euclidean geometries, nurb curves, fractal dimensions, anamorphic interpretations in the increasing dimensions of environment's representations, cellular automata and other tools which were structured for my generative software.
The results were endless variations of individuals belonging to the same artificial species, each one unpredictable but characterized by the same "artificial" DNA, as in Nature.
Starting from my first experiences of generative approach for designing artificial DNA of Italian medieval towns, made in 1987, until the last works in intelligent industrial productions and in cities identity design, this paper will follow the evolution of these mathematical tools for increasing in character and identity each variation.
Generative Art, Generative Design, Visionary Variations, Anamorphic Representation, artificial DNA, non-linear systems.
1. Argenìa and Generative Art
1.1. Generative Art. Generative Art is the idea realized as a genetic code of artificial events.
The creative act has changed. Not only because of the use of new digital tools, but because their availability introduces a new philosophy. Design changes from forming to transforming. And this is a step towards the representation of the idea at a more open and involving level. As musical variations departing from a common theme, every form interprets, in the manifold of possible parallel results, a modus transformandi, an idea, visionary variations.
Today, in fact, we have technological tools to pass from the old-industrial production of cloned objects, to the production of unique objects. This is a new revolution. With equal costs the digital era can produce unique and unrepeatable objects that emulate Nature and the hand of the craftsman. The unique object becomes a new answer to contemporary cultural needs that have been underrated for a long time. It leads to a world in which each environment, architecture or artificial object mirrors the aura of uniqueness and unrepeatability of every person. In this epoch, in which the identity of natural beings is repeatedly attacked through cloning, the generative design approach to artificial worlds realizes an opposite trend. With this approach man can experience again, through the use of artificial intelligence, artificial life systems, and advanced technologies, the aesthetical and ethical pleasure in nature.
1.2. Argenìa. The structure of Argenìa essentially consists of a system with two different components: a system of codes of transformation and an organizational paradigm for the evolutionary dynamics. Both elements are absolutely essential for realizing an idea as a generative motor. The generative process (cycle 1-2-3-4-5 of next paragraph) uses algorithms managing the transformation and evolution inside a non-linear system, but not the evolution of the system itself. The IDEA is the evolutionary system. It uses generative algorithms for representing a particular subjective concept defined as process. Each generative project can generate, using a lot of parallel artificial lives, an endless sequence of possible parallel results for fitting the architect’s imprinting with the client’s needs. The system has not automatic upgrading (like genetic algorithms) because the aim is not optimising/homologising the idea-system but representing a subjective human creative identity with the fullness of all possible results. For this reason (cycle 6A, 6B) the upgrade is manually made by the architect. As in Renaissance, this upgrading activity is one of the most important human creative acts during the design process. The only one that, following subjective interpretation, is impossible to emulate with AI and AL.
Figure 1: Generated castles with the same “artificial DNA”
1.3. The structure of Argenìa.
1. Artificial DNA: algorithms that define multiple paths from an existing world towards visionary ones. This is a set of transforming rules (transformation code like natural DNA) that identifies the designer’s imprinting and vision. These algorithms are used in every project and are upgraded after increasing experience.
2. Project Paradigm that activates the evolutionary path. This setup of the system is made for each specific design occasion, fitting the design occasion. It plans contaminations, interactions, interferences, resonances and exceptions.
3. Artificial life for increasing complexity that is the result of subsequent cycles of increasing complexity. Each generated event was not necessary before but becomes necessary after its generation. It is an irreversible temporal process; it is the clock of design evolution. The cycles continue until they reach the complexity that is requested by the architectural concept.
4. Results, endless visionary variations. Each one is unique and different. Although each result is unpredictable, it can be recognized as following the IDEA/species.
5. Choosing among different results. The selected scenarios will be used to upgrade the generative project and to generate a new set of results. The aim is to fit the client’s needs and to develop the architect’s concept.
6A.Feedback to #1 for upgrading/increasing transforming rules
6B.Feedback to #2 for upgrading evolutionary paradigm
Figure 2: Generated chairs with the same “artificial DNA”
1.4. The codes of transformation
The code system can be compared to the natural structure of DNA. The whole structure of rules is a matrix device that defines how to evolve a system towards complexity. In other words, one can consider it as a group of concepts that trace and identify a specific design behavior. In the case of Argenìa, since my first years of study I have deepened and developed my interpretation of the world of the Renaissance masters . These rules mirror my concept of the beauty of Nature. They represent my subjective fascination for some particular natural structures, whose harmony is translated into rule systems.
These rules are not objective, neither do they originate from a philological approach. As a whole, they represent my concept of harmony, which was born from my personal and cultural experience, from my reading of the universe of natural and artificial events where a visionary variation can rise. This approach is close to the Renaissance spirit and to its challenge: the interpretation of natural harmony as an operational code for realizing an artificial world, “la città ideale” . They perform a poetic structure.
This is a set of transformation codes of evolutionary logics that comes from tradition and from the inseparable synergy between the artistic and scientific approach. In fact, by experimenting with the evolutionary logics of complex systems, we are able to look for fragments of our code of harmony fathoming the Possible, seeking for our idea of beauty. The system’s non-linearity, and its realization of unpredicted exceptions, represents an unexpected synergy among non-connected parts of our aesthetical research.
Figure 3: Generated portraits “d’après Picasso” with the same “artificial DNA”
In searching for rules as codes of harmony, I have experimented with geometric, perspective and mathematical codes, which were visualized and made operational by computers. Perspective, Anamorphic representations and inverse perspective  were the main topics of my designing codes. In the methodological approach of the visionary anamorphosis builds figurations of the possible through the subjectivity of a vision. The plurality of anamorphic interpretations of events is a tool to produce plurality of similar events in the following dimension, producing a code of a species. Anamorphic reading of a bi-dimensional event produces, through successive interpretative actions, a plurality of three-dimensional events of the same kind. This is a basic tool of the Generative Design, Argenìa.
The images of art, from Simone Martini to Van Gogh, from Paul Klee to W. Kandinski, read through subjective interpretations based on the transposition from the Euclidean geometry to the non-Euclidean one, produce plurality of visions that show possible worlds, a genetic-interpretative code that characterizes and identifies the variations despite their oneness. 
In particular, I have made transformations by using imaginary numbers, what has enabled me to identify the role of events within a complex system. In comparison to parallel events, this system could be transformed and evolved along one “preferential path”, which, through possible variations of the subsystems and of the details that represent it, implies a logic of paradigmatic control over the whole and its identity. I have also used multidimensional cellular automata for writing rules that define the topological structure of generated architectural scenarios.
In order to build individual events, this artificial DNA needed an evolutionary system, an artificial life, which allowed it to develop and achieve the levels of complexity proper of our time.  The goal was the figuration of complex events, such as cities, buildings, industrial objects. It was not enough to produce beautiful and fascinating forms that allude to the natural complexity of possible environments, as for instance fractal or numerical wholes, represented by Bezier curves. My challenge was to produce artificial individuals that were "recognizable"  within the complexity of the existing events: historical cities such as the Italian medieval cities, New York whose identity is also recognizable in the most marginal areas, Chicago with its ability to represent the history of the architecture of the twentieth century, Hong Kong with its unrepeatable mixture of west/east styles, L.A., Washington D.C,, Milan, whose codes are focused on Futuristic tradition, and so on . I have begun my experimentation in 1986, starting from the Italian medieval cities.
Figure 4: Generated visionary variations of Futurism Museum in Milan.
1.5. The evolutionary paradigm
In order to reach the figuration of complex events, it was necessary to work out paradigms that used and guided the evolutionary structure of the system. In order to create these organizational paradigms, I needed to systematize the structure of the architectural space and objects, as Renaissance architects have done. Therefore, I built a system in which relationships among architectural events are nested inside each other. This system formed a basis for the evolutionary structure and its exceptions. (Exceptions are important because they could overturn deeply the same structure during the evolutionary path.)
The system is made up of event-spaces with, all around, 26 synapses, which manage the interface with possible topologically near events. The whole system is therefore based on the number 27. Every direct relationship between two spaces can maximally activate 9 complex interfaces. Every spatial event therefore has one to nine parallel possibilities for structuring a relationship with the topologically near event. Every interface, to operate its own evolution-transformation, is characterized by a series of parallel systems which are usable together and which can be reciprocally contaminated. Each of these systems responds to specific characters that the event will have to explain and show. Each one has a different geometrical-topological structure representing its peculiarity. For instance, one of the evolutionary contaminations that have been used in some architectural generative projects works with three parallel geometric systems. The first one is based on the number nine (9x9x9 references linked with specific relationships, such as the golden section), the second on the progressive division of axis and diagonals, and the third one replaces the Cartesian coordinates by the polar ones building an order of preferential relationships with centre or other relevant points. The contaminations and the interferences between these three parallel systems simultaneously generate complexity and harmony.
The system, in addition, provides some foldings that can alter the structure of topology making to coincide in a single event the interface produced by synapses, which are, before folding the system, distant one from the other. In this entire transforming path, time enters as a conclusive factor of the possible bifurcations of the evolutionary structure as it is the only unpredictable element. Every possible start-up of generative paths is conditioned from the temporal moment of its beginning, that is obviously always different. And the folding of the system, with the respective acceleration or induced decelerations, manages the unpredictability of the results.
This approach makes it impossible to repeat the same generation. This uniqueness is due to the temporality of the generative process that was started up, and it can only be overcome by producing clones through manipulating and resetting the clock, which is, of course, antithetical to the aim of the generative approach.
Once the architectural spatial net is systematized, I have built, referring to every single design occurrence, the logical plot to check the evolutionary dynamics of the system in order to fit the client’s needs. In other words, if the generative project has to realize a multifunctional skyscraper in Los Angeles or, for instance, a chair, it is necessary for the codes of harmony to work in such a way, as to reach this goal. This part of the generative project is obviously built ad hoc for every single project. Therefore, schematically, we do not have a homologating technology.
The generative projects are not tools for producing any possible result. The generative projects need a subjective approach in line with the humanistic tradition. It is possible, instead, to define a modus operandi and to make it executable through rules, as I have experimented in didactics. But this needs a further examination.
 Leonardo da Vinci, Essay of Painting, “... the artworks that the human eye commands to the hands are endless, as painters show in the representations of endless forms of animals and grasses, plants and sites”. Logic is the plane of invention.
 GA2002 Proceedings, Celestino Soddu, La città ideale, Generative Codes Design Identity. A city’s Identity can be represented with an open system of transformation rules, of developing procedures able to identify how each city performs its increasing complexity, how it creates its own future.
 Florenski, Inverted perspective. The possibility of representing the world surrounding us through codes that allude to infinity. The perspective tools become mirror of ourselves when we read with anamorphic approach the geometry of what surrounds us.
 Celestino Soddu, L’immagine non euclidea, (The Non-Euclidean Image), Gangemi Pub. Reggio 1987
 Complexity. Piranesi reaches complexity through the progressive layering of subsequent engraving on the same plates, by transforming and not by deleting and making again. Complexity is reached through the progressive layering of subjectivity, of subsequent interpretation of lived processes.
 C.Soddu, “Recognizability of the idea: the evolutionary process of Argenia” in P.Bentley & D. Corne, "Creative Evolutionary Systems", Morgan Kaufmann Publisher, San Francisco US, 2001, pag. 114.
 Visionary Variations by Celestino Soddu, personal exhibitions at Hong Kong Museum, Visual Art Centre, 2002, IDB Cultural Center, Inter American Development Bank, Washington DC, 2003, Pacific Design Center, Los Angeles, 2003, IFC Hong Kong 2004, Palazzo Giureconsulti a Milano, 2005
 Celestino Soddu, Citta’ Aleatorie, (Unpredictable Cities), Masson Publisher, Milano 1989
 C.Soddu, E.Colabella, Il progetto ambientale di morfogenesi (The Environmental Morphogenetic Design), Esculapio Publisher, 1992
 Generative Art annual conference Proceedings, chair Celestino Soddu , 1998-1999-2000-2001-2002-2003-2004. www.generativeart.com
 Celestino Soddu, Milan, Visionary Variations, Gangemi Publisher, Rome 2005