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Asaf DeganiNASA Ames Research Center, Moffett Field, CA [email protected]
Structure Preserving Transformations: Integrationof Two Patterns into a Whole
Basic Polygon(tile) for 1st Center
Basic Polygonfor 2nd Center
Another Basic Polygonfor 2nd Center Basic Polygon
for 3rd CenterSmallest Polygon Structure Preserving
Transformations: Nature’s WayStructure Preserving
Transformations: Tilework Design
Spillover: Two opposing Fleur-de-lis establish a link
1st CenterBegins to Develop
and Branches Out
into Adjacent Centers
by Linking on Geometrical forms
Adjacent star centers intensified
Made intense with color
Linking star centers by blue circles
Proliferation of interconnected patterns
Another pattern coming in around star center
Race track forms between new pattern and existing star center
2nd Center
Strengthening the star center
Intensified with spades, chevrons, fleur-de-lis, and the three arrowheads
A new center made of three arrowheads
Strengthening the new center with color
Connecting to adjacent star centerswith 3 blue circles and forming an (almost) complete
circle of fleur-de-lises and spades
Multitude of Centers working togetherto create a sense of wholeness
Alexander, C. (2002a). The Phenomena of Life.Berkeley, CA: The Center for Environ-mental Structure, p 33.
The work presented in this poster is an initial attempt to understand how information is organized so as to create order. The focus is on how geometrical forms come together in an integrated way and the kind of properties that facilitate order. The exploration is inspired by medieval art and science, where mathematical and geometrical aspects of order and wholeness were studied and applied to architec-ture and ornament design. In pursuing the problem of integration and organization of information, we are building on Christopher Alexander’s “theory of centers.” This theory, which is based on his career-long analysis of medieval architecture, provides a language and a methodology for achieving integration and organization in geometri-cal forms and architectural spaces. In addition, Alexander’s theory describes an evolving continuum for creating coherent spaces and intensifying them with details through what he defines as “structure-preserving transformations.”
ReferencesAlexander, C. (2002a). The Phenomenon of Life. Berkeley, CA: The Center for Environmental Structure.
Alexander, C. (2002b). The Process of Creating Life. Berkeley, CA: The Center for Environmental Structure.
Alexander, C. (1993). A Foreshadowing of 21st Century Art: The Color and Geometry of very Early Turkish Carpets. New York: Oxford University Press.
Blair, S. (1986). The Ilkhanid Shrine Complex at Natanz, Iran. Harvard University: Cambridge, MA.
Blair, S. (1983). The Octagonal Pavillion at Natanz: A Reexamination of Early Islamic Architecture in Iran. " In Oleg Grabar"(ed.). Muqarnas I: An Annual on Islamic Art and Architecture. New Haven: Yale University Press, 69-94.
Degani, A., Jorgensen, C., Shafto, M., & Olson, L. (2008). Extraction, Abstraction, Integration, and Organization of Information: Approach and Early Work. NASA Technical Memorandum 2008-214576.
Degani, A., Shafto, M. & Olson, L. (2006b). Data Abstraction and Integration of Information for Display: Analysis of Pilot-Automation Interaction. Proceeding of the 11th International Conference of Human-Computer Interaction in Aeronautics. pp. 164-167. September 20-22, Seattle, WA.
Grabar, O. (1992). The meditation of ornament. Princeton, NJ: Princeton University press.
Krishnamurti, J. (1929/1996) Total Freedom: The Essen-tial Krishnamurti. San Francisco: Harper Collins, p. 1. The devil and friend of his where walking down the street. They saw ahead of them a man stoop down and pick up something from the ground, look at it, and put it away in his pocket. The friend said to the devil, "what did that man picked up?" "He picked up a piece of Truth," said the devil. "That is a very bad business for you, then," said his friend. "Oh, not at all," the devil replied, "I'm going to let him organize it."
Michaud, R., Michaud S., & Barry, M (1996). Design and Color in Islamic Architecture: Eight Centuries of the Tile-Maker's Art. New York: Vendome.
Ozdul, Alpay (1995). Omar Khayyam, Mathematicians, and Conversazioni with Artisians. Journal of SAH 54:1 p.54-71.
Rasmussen, J. (1986). Information Processing and Human-Machine Interaction: An Approach to Cognitive Engineering. New York: North-Holland.
Rumi, J. (1273). The Mathnawi. IV, 2881-2887. Edited and translated by R. A. Nicholson, 1925-1940.
Salingaros, N. (1995). In defense of Alexander. HALI: the international magazine of antique carpet and textile art. Volume 78 pages 67-69.
Tucci, 1961/2001. the theory and practice of the Mandala. Mineola, NY: Dover.
Development of a Mouse Foot
Graphic Design by Cheryse Triano,TopSpin Design Works
(in the space between the 3 centers)
�e revealed painting is for the hidden picture... and this exists for another picture... until the third and fourth and fifth... until we understand the symbolic lesson inherent in it.
The Ilkhanid Shrine Complex, Photo Credit: Sheila Blair & Jonathan Bloom
Tiled hood of niche on inner left side, Photo Credit: Nandini Bagchee
Photo Credit: Sheila Blair & Jonathan Bloom
Photo Credit: Roland Michaud & Sabrina Michaud
Super-imposition of the basic polygon for the 3rd center on the structure creating a flower-like arrangement.Photo Credit: Sheila Blair & Jonathan Bloom
The pyramid-like framework advocated here for analyzing information organization stems from the observation that there is a stepwise progres-sion in the way signals (from the environment and/or the underlying system) are captured as data, then abstracted in the context of the user’s tasks to meaningful representations (e.g., indications and icons) on a display. In domains such as aviation and space flight, the complexity of the underlying systems is such that many components and their corre-sponding data and information are physically interrelated (e.g., an increase in a chamber’s temperature results in an increase in pressure). Presenting these interrelationships by integrating geometrical forms into structures of information is critical for improving users’ understanding of current and impending situations. When these structures of information are organized into a whole, emerging patterns are revealed, providing the so called “big picture” that pilots and astronauts strive for.
– Rumi, J. (1273).
Photo Credit: Sheila Blair & Jonathan Bloom
Photo Credit: Sheila Blair & Jonathan Bloom
Alexander, C. (2002b). The Process of Creating Life. Berkeley, CA: The Center for Environmental Structure.pp. 124-125.
Nevertheless, creating a visual display that is well integrated and organized is a very difficult task. Projecting a sense of wholeness such that interrelationships become apparent and users can intuitively “understand” the dynamics of the system and be sensitive to anoma-lies is also quite a challenge. Cockpit display of sub-system informa-tion is certainly one area that is in much need for integration and organization, but there is no tradition or theory today to guide design-ers in creating such “integrated displays.” To this end we examine the artifact portrayed in this poster to try and understand how its geo-metrical elements come together. We then touch on the levels of abstraction, integration, and organization that appear to support the sense of wholeness that emanates from it.
The tilework was constructed sometime between 1304 and 1307 AD and is made from tile, paint, and stucco. It appears at the entrance to a Sufi convent in the oasis town of Natanz, present day Iran, and portrays multiple patterns that are woven together to create a complex and highly interconnected visual effect. Using Alexander’s theory, three main centers were identified: one is around the dark star, the second is at an intersection of the stucco pattern, and the third is marked by three chevrons-like forms. After tracing the design by hand, to intuitively understand how patterns integrate to create a whole, one begins to feel a sense of repetition. Highly condensed geometrical forms arise unexpectedly from the design: We find that around each center revolves at least one “basic polygon” which also defines a grid. When each one of the basic polygons is rotated and/or flipped along the grid, it can generate the entire visual field. One of the interesting properties to emerge is that the area delineated by the three main centers forms the smallest polygon capable of generating the field.
In addition to these geometrical properties that lie underneath the revealed picture, the artifact exhibits elements of abstraction, integra-tion, organization, and compression. Abstraction can be seen in the way the visual field appears as a constellation of stars or floral formations (or both). Integration is evident in the way geometrical forms are woven together around each center; another level of integration exists in the linkages between centers (e.g., the diamond between the dark star-like centers). A hint of wholeness appears in the way patterns, which contain elements from different centers (e.g., the figure eight-like racetracks), emerge in a visually coherent and cohesive way. Compression exists in the way the entire field can be generated by increasingly small polygons that at first glance appear irrelevant and indistinct.
and so on...
Asaf DeganiNASA Ames Research Center, Moffett Field, CA [email protected] work presented in this poster is an initial attempt to understand The pyramid-like framework advocated here for analyzing information Nevertheless, creating a visual display that is well integrated and The tilework was constructed sometime between 1304 and 1307 AD and is made
SOME PROPERTIES OF MULTILAYERED PATTERNS (OF INFORMATION): Insights from Medieval Architecture
Several preliminary observations can be drawn from this analysis. First, an intense and highly organized visual field contains several centers that are linked together by means of unique geometrical forms. Second, Alexander’s structure-preserving transformation can be observed in each of the three cen-ters, and appears to support the basic polygons that revolve around them. Third, the centers support patterns that crisscross the visual field; some of which are made of elements from distinct centers (e.g., the figure eight racetracks) creat-ing a combined, or integrated, pattern. Fourth, the emergence of multiple patterns and the existence of manifold grids opens the door into the so-called “information spaces.” And finally, the artifact’s visual field can be condensed within a very small polygon, which contains all the information necessary to generate the whole—an observation which may have implications for the design of future adaptive interfaces that need to be transmitted to remote sites.
To conclude, the research effort described here explores the extensions of Alexander’s theory into the realm of information spaces where it becomes feasible to infuse, compact, and visualize interconnections among large amounts of data and information. The intended application of this research is in the design of information systems for aerospace applications such as airline cock-pits and NASA’s mission control centers. We believe that properties of organi-zation and order that exist in medieval artifacts can be efficiently employed in the presentation of modern information systems, highlighting interrelationships between data points as well as sets of data and information. With further study, it may be possible to generate the kind of information spaces that are inherent in medieval artifacts in order to house large amounts of modern data. We hope that such exploratory studies will also help support the perceptive and intuitive faculty necessary to design the integrated displays of the future.
The first basic tile can be used to construct the field as it completely tiles the space around the niche. Such a construction scheme relieves the craftsman from worrying about local accuracy of lines and shapes as the global accuracy of the field will always be maintained. It also allows for another level of information seen in the non standard “ease of the stroke.” In the case shown here with a green circle, we see a local deviation from the shape (diamond) which may serve to point our attention to the “three arrowheads” center. Adding a sense of humanness into what could have been a very stringent geometrical arrangement (if it was followed precisely or done on a modern computer, e.g.).
A conceptual framework. The pyramid in the figure has five levels: (1) extraction of signals from the system and its
environment and turning them into data; (2) abstraction of data into corresponding information; (3) integration of information into
geometrically coherent structures so as to show meaningful relationships, supporting knowledge and understanding; (4) organization of these information structures in order to create a sense of wholeness; (5) compression, which
is the outcome of order and wholeness, is the key for opening information spaces.
Horizontal flip of the tilework to reveal the whole. The original tile only shows a partial pattern. It was probably erected in this (partial) way so that the viewer's mind has to complete the picture. This is one category of compression.
Organization of the engine parameters interconnected with eight other sub-system to create a whole where multiple linkages are made available as well as compos-ites of parameters (pairs, triplets, quadruples) of one system as well as composites made up of parameters of related sub-systems (Degani et al. 2008).
Super-imposition of the polygon for the 1st center on the structure. The polygon tiles it completely.
INFORMATION SPACES
ORDER & WHOLENESS
STRUCTURES OFINFORMATION
INFORMATION
DATA
SIGNALS
1. Extraction
2. Abstraction
3. Integration
4. Organization
5. Compression
