Generative Dynamics: Process, Form and Structure


Manuel A. Báez, Architect, B. Arch., M. Arch.

Co-ordinator: Form Studies Unit and Undergraduate Program

School of Architecture, Carleton University, Ottawa, Ontario,  Canada






The “Phenomeno-logical Garden: A Work in Morpho-logical Process” is an on-going architectural project that is exploring the morphological, integrative and generative potential of fundamental processes that correlate with the rich and diverse world of natural phenomena.  Through the emergent properties of “woven” flexible membranes (or networks) that perform as highly coordinated-cellular-arrangements of basic elemental relationships, a variety of forms, structures and installations have been fabricated and exhibited in several institutions.  The evolving project is a systematic investigation of the versatile and generative potential of these dynamic processes that are found throughout systems in nature, biology, physics, mathematics, cognitive science and music.  As part of the objectives of the Form Studies Unit in the School of Architecture at Carleton University, the work seeks to investigate how complex forms and structures are generated from initially random processes that evolve into morphologically rich collective relationships.

The morphological diversity revealed by this working and teaching method offers new insights into the complexity lurking within nature’s processes as revealed through modern scientific theories of Chaos, Complexity, Fractal Geometry and Cellular Automata.   These developments and working process also offer insights into the design and philosophical aspirations of such key central figures in the formative period of modern architecture as Antoni Gaudi, Louis Sullivan, Frank Lloyd Wright, Le Corbusier, Buckminster Fuller, Frei Otto and, more recently, the architect/engineer Santiago Calatrava.  The implications of these developments are relevant to the study of morphology, architecture and other diverse disciplines at a time when the ideas emerging out of our deeper understanding of complex phenomena throughout the physical world are being embraced for conceptual and philosophical inspiration.



1. Introduction


“Think not of form, but of the act of forming.”                                                       Paul Klee


“We have been trained to think of patterns, with the exemption of those in music, as fixed affairs.  It is easier and lazier that way but, of course, all nonsense.  In truth, the right way to begin to think about the pattern which connects is to think of it as primarily (whatever that means) a dance of interacting parts and only pegged down by various sorts of physical limits and by those limits which organisms characteristically impose.” [1]

Gregory Bateson, Mind and Nature

“Music, like architecture, is time and space.  Music and architecture alike are a matter of measure.”

“How to divide into sections the continuous phenomenon of sound?  How to cut up sound in accordance with a rule acceptable to all, but above all efficient, that is, flexible, adaptable, allowing for a wealth of nuances and yet simple, manageable and easy to understand?” [2]

Le Corbusier, The Modular 


 “Morphology is not only a study of material things and the forms of material things, but has its dynamical aspect, under which we deal with the interpretation, in terms of force, of the operations of energy.”[3]                           

D’Arcy Wentworth Thompson, On Growth and Form


Nature’s fundamental processes inherently generate regulatory systems and patterns that correlate with the rich realm of natural phenomena.  These fertile processes inherently involve elemental relationships that dynamically evolve into integrative systems with startling form and structure generating capabilities.  Through the aid of modern computer visualization and analyzing techniques, we are gradually acquiring deeper insight into the ways the “operations of energy,” referred to by D’Arcy Thompson above, interweave into dynamic cellular systems and structures that often recall the patterns and motifs found in nature, art, architecture, mathematics, biology, physics and music.  Gregory Bateson’s description of patterns and their interrelationships, along with Le Corbusier’s requirements for the measure of a continuous phenomenon such as sound are examples of dynamic conceptions very similar to what is presently being revealed about the nature of natural processes and associated cellular systems.


2. Generative Self-organization


Through the analysis of the generative potential and interrelated cellular patterns of these natural process-systems, more comprehensive insight can be achieved regarding emergent complex behaviour and morphology.  Intrinsically, these processes-in-formation are highly coordinated cellular relationships that are simultaneously stable, highly dynamic, self-organizing, and fluently encoded with in-formation. Self-organization is generated and/or emerges from the resolution of the dynamic interactions throughout the system.  The “Bénard cells” shown in Figure 1 are a classic example of self-organization resulting from the flow of heat through a liquid, gas or, as in the example shown, smoke.  Initially, the smoke forms folds, waves and rolling cloud-patterns that, at a certain threshold, suddenly self-organize into cellular convection currents.  In this critical state, the dynamic cellular pattern is highly sensitive to any disturbance and will re-organize itself as it resolves the instabilities resulting from any fluctuations (see Figure 1 B).  The overall toroidal form of each cell (hexagonal under ideal conditions) is stationary and stable while, simultaneously, the smoke dynamically circulates throughout the form.  “Benard cells” and other such complex phenomena are encoded with highly adaptable patterns of dynamic processes-in-formation.  The probing of such event-filled networks and their associated cellular units can reveal new insights into the nature of the reciprocal relationship that exists between matter, developmental processes, growth and form.

Figure 1:  Bénard Cells, pattern of cells generated with a thin layer of smoke between a hot and cold surface.  A: Field of “rolling” torus cells: smoke rolls within each individual toroidal form, B: Cells are “sheared” by sliding one surface over the other from left to right. From On Growth and Form [3].









3. Phenomeno-logical Garden


Figure 2 provides an overview of the “Phenomeno-logical Garden: A Work in Morpho-logical Process” project.  Overall, the project has been inspired by the morphological and philosophical implications of the developments described above.  The images on the upper right and left sides, as well as the undulating central line (or path), are of an earlier project whereby a potter’s wheel was used to spin a suspended cotton string into initially stable and sequential wave-formations that became turbulent at higher speeds.  This project, entitled “Ariadne’s Thread/Rumi’s Ocean” [5], was inspired by scientific investigations of dynamic phenomena and initiated the “Phenomenological Garden.  It was recorded from different vantage points, generating a wealth of morphological formations, generative working procedures and insights into the correlation between perception and frame of reference.  Shown on the upper right-side of the Figure is a collage of three-dimensional forms generated by the spinning string.  At times the whirling string would be spinning at a rate whereby it would cast shadows of itself on its generated surface (Fig. 2 upper left- side). 


3.1 Works-In-Process

Through extensive research and analysis of the work generated from such projects as the one described above and the conceptual developments that inspired them, the dynamic flexibility and versatility of several elemental geometric relationships were explored by incorporating a flexible joint as part of the assembled arrangement.  These elemental relationships can be found within the inner structure of nature’s resolutions to dynamic phenomena.  The underlying woven stress patterns found superimposed and interacting within the inner structure of bones, is a biological example of the way nature resolves a dynamically complex structural situation.  D’Arcy Thompson referred to these self-organizing stress fields and patterns as a “diagram of forces” [3]


Figure 2: ©Manuel A. Báez, “Phenomeno-logical Garden: A Work in Morphological Process,” 1991- Present, portion of the conference poster.  Upper right-side: collaged three-dimensional string formations; upper left-side: three-dimensional string formation with shadows of the spinning string on the generated surface; lower left-side: initial cellular units and cellular arrangements (see Figure 3 below for other units); middle right-side: collaged undulating string with scattered forms and structures developed from various flexible cellular units as those shown in the lower left-side.











generating the form of an object.  The flexible joint consists of two bamboo dowels joined together, at this exploratory phase, with a rubber band, thus allowing for a high degree of flexibility.  Through a variety of diverse arrangements of several of these joints, very versatile cellular units have been conceived and their form generating potential explore by joining (or weaving) them together into membranes or fabrics.  The cellular units shown in the lower left side of Figure 2 and in Figure 3 are at different stages of their complex development.  The flexibility of the joints and their three-dimensional arrangements, both within an individual cell and throughout the cellular membrane, generates a wealth of possible forms and structures through the emergent transformative and self-organizing properties of the integrated assembly. These emergent properties are similar to the inherent properties of the natural phenomena that inspired their conception.  The methods through which the membrane is explored and segmented, will determine the forms and structures that can be discovered and developed. The hands-on experience is that of a process whereby one feels, follows, flows with, and guides the versatile form-generating and self-organizing properties of the dynamic relationships.  Gradually it becomes apparent that a square geometric arrangement is one of the most versatile cellular units.  Figure 4 shows a membrane (upper left-hand corner) using this unit with more elaborate developments shown in the lower left and right sides.  The upper right-hand corner shows an inherently coiling structure (approximately 30' in length) with several installations of this structure shown in Figure 5.  Figures 6 and 7 show different views of a more complex installation done with this square cellular membrane.  The installtion was part of a symposium that I was invited to conceive and organize at Cranbrook Academy of Art for the Sybaris Gallery in Michigan, USA.  The symposium, entitled Metaphoric Interweavings, explored the interrelationships between weaving, musical composition and architecture through the use of a cellular or modular compositional process.  Figures 8, 9, 10 and 11 show some of the forms, structures and installations produced through this working process in the Crossings Workshop.  As part of the evolving “Phenomenological Garden,” these works-in-process continue to explore the complex forms and structures that can be developed through this morphologically rich generative process.



Figure 3: ©Manuel A. Báez, Crossings Workshop, Suspended Animation Series: Cellular Form Studies, 12" bamboo dowels joined together with rubber bands.  These initial cells and cellular arrangements are woven together into flexible membranes.  Different cut-out patterns of the membranes will generate different forms and structures through the inherent flexibility of the integrated assemblies.




Figure 4: ©Manuel A. Báez, Suspended Animation Series: Cellular Form Studies with square cells, 12" and 6" bamboo dowels joined together with rubber bands, 1994-present.  Upper left-hand corner shows a portion of the membrane used throughout all fabrications shown in Figures 5, 6 and 7.







Figure 5: ©Manuel A. Báez, Suspended Animation Series: Installations at Cranbrook Academy of Art, bamboo dowels and rubber bands, 1998-2000. Fabrications with square cellular unit membrane shown in Figure 4 and the coiling structure shown in the upper right-hand corner (fig. 4).







Figure 6: ©Manuel A. Báez, Phenomenological Garden Installation for the Metaphoric Interweavings Symposium at Cranbrook Academy of Art, bamboo dowels & rubber bands, 1998.   Two columns are transformed into an intricately patterned ceiling structure.  Emergent patterns are revealed as one walks around the installation or, as shown in the lower right, as one looks into the central mirrored table shown on the left.  Fabrications with square cellular units and membrane shown in Figure 4.



Figure 7: ©Manuel A. Báez, Phenomenological Garden Installation for the Metaphoric Interweavings Symposium at Cranbrook Academy of Art, 1998.  Columns are transformed into an intricately patterned ceiling structure with different emergent patterns revealed as one walks around the installation.








Figure 8: ©Manuel A. Báez, Crossings Workshop, Suspended Animation Series: Kosoussevitzky Art Gallery Installation, Pittsfield, MA, USA, 2001.  Cellular Form Studies, bamboo dowels and rubber bands.  Works by Mariam Shaker and Sherin Rizkallah.



Figure 9: ©Manuel A. Báez, Crossings Workshop, Suspended Animation Series: Cellular Form Studies, bamboo dowels and rubber bands, 2001-02.  Works by Diana Park, Sherin Rizkallah, Sahar Kuba, Daniel Cronin and Sharif Kahn. Left side structures: w/ heptagonal cells; upper middle & right-side: w/pentagonal cells; lower middle & right-side: w/square cells. 





Figure 10: ©Manuel A. Báez, Crossings Workshop, Suspended Animation Series: Cellular Form Studies, bamboo dowels with plastic tubing joints, 2004.  Works by Natalia Kukleva and Nathan Dykstra.  Left side structure (top and side view) with square cells; right side structure with pentagonal cells.







Figure 11: ©Manuel A. Báez, Crossings Workshop, Suspended Animation Series: Crossings Workshop, Suspended Animation Series, Shadow Casts: Cellular Form Studies, bamboo dowels and rubber bands, 2002.  Work by Diana Park with heptagonal cells.








4. Conclusion


As part of his lecture on “exactitude” published in Six Memos for the Next Millennium, the Italian writer Italo Calvino offers us the following observations and advise:


“Among the scientific books into which I poke my nose in search of stimulus for the imagination, I recently happened to read that the models for the process of formation of living beings ‘are best visualized by the crystal on one side (invariance of specific structures) and the flame on the other (constancy of external forms in spite of relentless internal agitation).’

What interests me here is the juxtaposition of these two symbols, as in one of those sixteenth-century emblems . . . .  Crystal and Flame: two forms of perfect beauty that we cannot tear our eyes away from, two modes of growth in time, of expenditure of the matter surrounding them, two moral symbols, two absolutes, two categories for classifying facts and ideas, styles and feelings. . . .  I have always considered myself a partisan of the crystal, but the passage just quoted teaches me not to forget the value of the flame as a way of being, as a mode of existence.  In the same way, I would like those who think of themselves as disciples of the flame not to lose sight of the tranquil, arduous lesson of the crystal.” [5]


The richness of nature’s processes challenges our imagination because of its complex simplicity.  This paradox has inspired the work of Leonardo Da Vinci, J. W. von Goethe, Frank Lloyd Wright, Le Corbusier and countless other creative individuals.  Italo Calvino was also inspired by this tradition and was well aware of modern developments in science.  These developments, along with the history of science and its relationship with literature and philosophy, were a source of inspiration for his creative imagination.  To Calvino the Crystal and Flame symbolize the paradoxical and contradictory nature of matter as revealed to us in the twentieth century.  This correlation between form and process, as well as, simplicity and complexity has been revealed to us periodically throughout history.  “This is common to all our laws;” states the physicist Richard Feynman, “they all turn out to be simple things, although complex in their actual actions.” [6] The work-in-progress presented here inherently addresses this fundamental paradox through an integrative working process.  Such a process can offer new directions to the fields of morphology, architecture and other disciplines at a time when the ideas emerging out of our deeper understanding of complex phenomena are being embraced for conceptual inspiration.  The way towards the rich realm of diversity, as nature shows us, is through simple fundamental rules that eventually lead to a paradox of constrained and versatile freedom.





[1] Bateson G (1980) Mind and Nature, New York: Bantam Books.

[2] Le Corbusier (1958 ) Le Modulor, London: Faber and Faber.

[3] Thompson DW (1992) On Growth and Form, Complete Revised Edition, New York: Dover Books.

[4] Ariadne is the mythological Greek guide to the labyrinth of chaos and the individual life.  Jalai al-Din Rumi is the Great Persian mystic poet of the thirteenth century and the creator of the whirling, circular dance of the Mevlevi dervishes.

[5] Calvino I (1988) Six Memos for the Next Millennium, Cambridge, Mass.: Harvard University   Press

[6] Feynman R (1967) The Character of Physical Law, Massachusetts: The M. I. T. Press.