Generative Logic in Digital Design
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Generative Logic in Digital Design Robert H. Flanag an University of Colorado, USA rflanag [email protected] This exploration of earl y-stage , arc hitectural design pedagog y is in essence, a r ecord of an ongoing transformation underway in arc hitecture , from its practice in the art of g eom- etry of space to its practice in the art of g eometry of space-time. A selected series of stu- dent experiments, from 1992 to the present, illustrate a pro gression in arc hitectural the- ory, from Pythag orean concepts of mathematics and g eometry, to the symbolic r epresen- tation of space and non-linear time in film. The dimensional expansion of space, from xyz to xyz+t (time), r epresents a tactical and strategic opportunity to incorporate multi- sensory design variab les in arc hitectural practice, as w ell as in its pedagogy . Keywords. g enerative; process; derivative; logic; systemic. Generative Space Time Geometry In the 1980’s and 1990’s, Computer Aided Two additional design considerations Design automated the symbolic, geometric r epre- emerged from this study of geometric progression sentation of space, and it did so through the and generative principles: 1. Time emerged as a application of principles of modularity, iteration, dimensional design variable, described by the and recursion. Coincidentally, this created an geometry xyz+t; much as film incorporates non- opportunity for the digital designer to bypass the linear symbolic content as the message carrier, intended management functions of CAD, r epre- architectural design is capable of employing non- sentation and validation, and instead to expanded representational, symbolic means as its message its potential application of r ecursive and deriva- carrier. The multi-dimensional design require- tive design principles. For instance, Corbusier’s ments of xyz+t create an opportunity for a multi- “Modular Man,” the 20th century’s most identifi- sensory design interface. 2. Once this dimension- able architectural icon, addressed principles of al variable is available, sound is addressable. The self-similarity and proportion; the computer effort- periodic construction of sound diagrams, as in lessly and transparently applied these mathemat- musical scores, creates an opportunity for a com- ical and geometric r epresentations of modularity. mon interface and the simultaneous development Similarly, Frank Lloyd W right’s “organic” architec- of vision and sound in a coordinated multisenso- ture, one of the 20th century’s most identifiable ry design process. ar chitectural principles, was unburdened of its complex and laborious analytical r equirements; Precedent its generative potential in r ecursive and iterative principles, became r eadily addressable. “Architecture depends on order arrangement, eurythmy, symmetry, propriety and economy.” - Vitruvius (1st century B.C.) eCAADe 21 digital design 473 reflects a significant advance in implementation. Figure 1. 21st Century Man, Further improvements in generative design capa- by author. bilities followed in the curvilinear and modulated construction of the Coliseum c. 80AD. In these and other civic structures, the inherent beauty of the arch, its use in proportional modularity, and the application of advanced engineering con- cepts defined a standard of beauty and function that resonates through time. Sacred Architecture The first four hundred years of the new millen- nium A.D. witnessed the final advance, then grad- ual disintegration of the civic infrastructure of the Roman Empire; simultaneously, Christianity sub- sumed existing cultural values and mores. 800 years of theocratic adaptations, primarily of Roman precedent, transpired before a fully trans- formed Christian architecture was perfected. “In the Cathedral of Chartres the architect has r eal- ized the cosmological order of luminosity and Ancient Greeks attributed beauty to harmo- proportion to the exclusion of all other architec- nious principles of nature, a r eflection of the tural motifs and with a perfection never achieved gr eater universe, and applied these principles in before. Light transfigures and orders the compo- music, philosophy, and architecture. sitions in the stained-glass windows.… perfect Consequently, generative principles infused the proportion, harmonizes all elements of the build- proportioning systems of column design, building ing (Simson, 1988).” The cathedral operated as a construction, and even anthropomorphic embel- transcendental device according to the harmonic lishment. The Pythagorean, mathematical ratios of a divine universe with “God as its archi- approach “…leads to the use of a constant: a tect (Simson, 1988).” The device activated at con- module. It is the module – appropriate to each and secration in perpetuum, on behalf of penitents as every building - that makes it possible to obtain a device of salvation. eurhythmia … In expressing a higher r eality, they St. Augustine (354-430A.D.) prescribed design turn the temple into the material r ealization of principles for sacred architecture. This knowledge divine truth (Stierlin, 1997).” was required to construct the Cathedral, an Rome appropriated principles of proportional instrument of divine intervention operating at the modularity, expanded its application with intersection of the temporal and spiritual world. enhanced engineering capabilities, and improved The consecration of architecture of sacred pro- construction management systems. The harmon- portions activated the harmonic synchronization ic engineering solution of tiered and modulated between otherwise imper ceptible r ealms. St. stone arches in the 19BC Pont du Gard aqueduct Augustine organized music, architecture, geome- 474 eCAADe 21 digital design try , proportion, and sacred numbers into theolog- Space-Time Architecture ically sound generative systems of “perfect ratios” “…the source of all aesthetic perfection.” Corbusier needed to reintegrate time into Augustine’s unyielding and r estrictive rules of har- architecture – the expediency of productivity of monics and proportions provided the foundation the Industrial Revolution had negated the value of for development of a spiritual device constructed time in architecture. In r esponse, Corbusier devel- on earth – “…rendering it a place in which favours oped cubist techniques to symbolically r epresent are more graciously granted by God (Pontificale multidimensional aspects of space-time in art, “I Romanum).” (http://www .newadvent.org/cathen/ painted my first picture at the age of thirty-one, in 04276a.htm: May 2003). the fall of 1918 (Corbusier).” Picasso, along with Braque, founded cubist expression in 1907, Secular Architecture “Picasso and Einstein believed that art and sci- ence are means for exploring worlds beyond per- The Industrial Revolution signalled a signifi- ception, beyond appearance (Miller, 2001).” cant shift in the concepts of building and design; Drawing and paintings in the New W orld of the division of labour and the specialization of Space (Corbusier, 1948) reflect techniques devel- function began an inexorable transition away from oped by Corbusier so that architecture could the single harmonic reflection of a divine universe. “take possession of space.” Corbusier cagily In architecture, design principles r everted to the avoided crediting Einstein, Picasso and Braque, secular proportioning systems of the pre- except for oblique r eference to “[Those who] Christian era. Sacred principles in architecture spoke of the fourth dimension with intuition and gave way to the profane values of humanism, sci- clairvoyance.” While in the cause of Corbusier, “A ence, and finance – to the great consternation of life devoted to art, and especially to a search after the Catholic hierarchy. Throughout the 17th, 18th harmony, has enabled me in turn, to observe the and 19th centuries, secular design failed to same phenomena through the practice of three achieve stylistic consensus despite rapid techno- arts: ar chitectur e, sculpture and painting logical advances; until the emergence of (Corbusier, 1948).” Modernism, design expression found safety in Corbusier placed man at the centre of his atavistic reference to prior styles. design universe, “We pause, struck by such inter- It was Einstein’s momentous theories on r ela- relation in nature, and we gaze, moved by this tivity (1905) that r edefined the mechanics of the harmonious orchestration of space, and we r eal- universe and all that preceded it – in art, it creat- ize that we are looking at the reflection of light.” ed a foundation for Modernism. Corbusier, an Corbusier’s invention of the Modulor was a signif- architect of extraordinary intellect and talent, icant contribution to design implementation of his arrived at precisely the right time to exploit theories. Einstein’s r evolutionary concepts. “Just as r elativ- ity theory overthrew the absolute status of space Modularization and Harmonics and time, the cubism of Georges Braque and Picasso dethr oned perspective in art (Miller , The Modulor is a harmonic proportioning tool 2001).” used to r elate design to human scale. “A lifetime concerned with the play of proportion has led to a discovery which unites, in a single mathematical eCAADe 21 digital design 475 combination, numbers and the human figure. The logic. Natural systems are open: our knowledge of harmony r ecaptured by the Modulor would be them is partial, approximate, at best (Horgan, without salt if it were exclusively mathematical. 1995).” In this r elated discussion of artificial