Additional Links and References

The subject of "biological complexity" or "organised complexity" in the built environment is a rapidly developing one. Even so, this fascinating field has been around for at least half a century. Perhaps the most seminal texts are these classics by Jane Jacobs and Christopher Alexander:

Jane Jacobs, "The Kind of Problem A City Is," from The Death and Life of Great American Cities

Alexander, Christopher, "A City is Not A Tree," RUDI Online Resources.

Alexander has written many other works on urban complexity since then:

Alexander, Christopher et al. A Pattern Language (Oxford University Press, New York, 1977).

Alexander, Christopher et al. A New Theory of Urban Design (Oxford University Press, New York, 1987).

Alexander, Christopher. The Nature of Order (Center for Environmental Structure, 2004).

Alexander's site at the Center for Environmental Structure is:

http://www.patternlanguage.com

Our colleague Nikos Salingaros has a number of on-line papers on this topic, available at:

http://www.math.utsa.edu/sphere/salingar/contr.arch.html

Many other texts discuss complexity and "chaos theory" (a narrower term disliked by some scientists, since what is loosely called "chaos" is actually a different kind of order.) Following are some websites that offer an overview and links to additional resources.

A definition of complexity, and useful links, by Francis Heylighen of the Free University of Brussels:

http://pespmc1.vub.ac.be/COMPLEXI.html

A number of organisations and journals are devoted to this subject. Here are two:

http://www.complexity-society.com

http://journal-ci.csse.monash.edu.au

Here is one of the more lucid texts giving an overview of the subject:

Waldrop, M. Mitchell, Complexity. (Touchstone Books, 1992)

Additional texts on this and related subjects, particularly as they apply to design:

Bovill, Carl. Fractal Geometry in Architecture and Design (Boston: Birkhäuser, 1996).

Coveney, Peter and Highfield, Roger, Frontiers of Complexity: The Search for Order in a Chaotic World. (Fawcett Columbine, 1995).

Doczi, Gyorgi. The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture. (Shambhala Publications, 1994).

Ghyka, Matila. The Geometry of Art And Life (Paperback, 1988).

Gleick, James Chaos. (Penguin USA, 1988).

Miller, George, "The Magical Number Seven, Plus or Minus Two," Psychological Review, 63, 81-97 (1956).

Simon, Herbert, “The Architecture of Complexity,” Proceedings of the American Philosophical Society 106 1962 pp 467-482

Wolfram, Steven, A New Kind of Science (Wolfram Media (2002).

The implications of this science for the structure of society and culture has also been extensively discussed. Here is one of the more lucid texts:

Johnson, Steven. Emergence: The Connected Lives of Ants, Brains, Cities, and Software. (Scribner, 2001).

The evolution of culture as a complex phenomenon has been discussed by many authors. One of the most incisive papers on the evolution of "spurious" cultures was by the pioneering anthropologist and linguist Edward Sapir:

Edward Sapir, Culture, Genuine and Spurious

The philosophy of science behind much of complexity theory was explored early in the 20th century by the mathematician and philosopher Alfred North Whitehead:

Whitehead, Afred North, Modes of Thought. (MacMillan Free Press, New York, 1938).

Whitehead, Afred North, Process and Reality. (MacMillan Free Press, New York, 1929).

Whitehead, Alfred North, Adventures of Ideas. (MacMillan Free Press, New York, 1933).

Whitehead, Alfred North, Science and the Modern World. (MacMillan Free Press, New York, 1935).

Other philosophers who explored related ideas were Henri Bergson, William James and Charles Peirce.

Many mathematicians and anthropologists have recently made great strides in exploring the concept of "symmetry" in design. The notion of symmetry here is not merely axial symmetry, but a much broader conception including recursiveness, fractal forms and other geometries of the "new sciences." (See the closely related discussion of "connective symmetry" in "The New Modernity" in this volume.)

One of the most comprehensive bibliographies on the topic of symmetry is given in the fine recent book Symmetry Comes of Age: The Role of Pattern in Culture, edited by Dorothy K. Washburn and Donald W. Crowe. We reprint it here with thanks to the authors.

Arnold, Dean E.

1983 – Design Structure and Community Organisation in Quiana, Peru. In Structure and Cognition in Art. Dorothy Washburn, ed. Pp.56–73. Cambridge: Cambridge University Press.

1993 - Ecology and Ceramic Production in an Andean Community. Cambridge: Cambridge University Press.

Artz, Frederick B.

1962 – The Mind of the Middle Ages. 3^rd ed. New York: Alfred Knopf.

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1991 – Ethnomathematics: A Multicultural view of Mathematical Ideas. Pacific Grove, Calif.:Brooks/Cole.

2002a – The Kolam Tradition. American Scientist 90 (1):56-63

2002b – Mathematics Elsewhere. Princeton: Princeton University Press.

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1999 – The Self-Made Tapestry: Pattern Formation in Nature. New York: Oxford University Press.

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1995 – The Artful Universe. Oxford: Clarendon Press.

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1986 – Escherian and Non-Escherian Development of New Frieze Types in Hanti and Old Hungarian Communal Art. In M.C.Escher: Art and Science. H.S.M. Coxeter et al., eds. Amsterdam: Elsevier.

1989 – Symmetry and Technology in Ornamental Art of Old Hungarians and Avar-Onogurians from the Archaeolgical Finds of the Carpathian Basin, 7^th – 10^th Century A.D. In Symmetry 2: Unifying Human Understanding. Istvan Hargiitai, ed. Pp. 715–730. Oxford: Pergamon Press.

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1997 –Detection of Symmetry and Perceptual Organisation: The way a Lock-and-Key Process Works. Acta Psychologica 95:119-140.

1999 –Designing Tessellations: The Secrets of Interlocking Patterns. Chicago: Contemporary Books.

Bier, Carol

1992 – Elements of Plane Symmetry in Oriental Carpets. The Textile Museum journal 31:53-70.

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1990 – Universal Patterns: The Golden Relationship: Art, Math, and Nature. Rev.ed. Book 1. Bradford, Mass.: Pythagorean Press.

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1976 – Young Children’s Processing of Asymmetrical and Symmetric Patterns. Journal of Experimental Child Psychology 22:309-318.

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1963 – The Painter’s Secret Geometry: A study of composition in Art. New York: Hacker.

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1989 – The Geometry of Decoration on Prehistoric Pueblo Pottery from Starkweather Ruin. In Symmetry 2: Unifying Human Understanding. Istvan Hargittai, ed.Pp.731-749. Oxford: Pergamon Press.

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1991 – A Formal Approach to Design: Symmetry and Beyond. In The Ceramic Legacy of Anna O. Shepard. R.Bishop and F. Lange, eds. Pp. 280-320. Boulder: University Press of Colorado.

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1989 – In the Tower or Babel: Beyond Symmetry in Islamic Design. In Symmetry 2: Unifying Human Understanding. Istvan Hargittai, ed. Pp. 751-789. Oxford: Pergamon Press

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1986 – M.C.Escher: Art and Science. Proceedings of the Interdisciplinary Congress on M.C. Escher. Amsterdam: Elsevier.

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1986 – Symmetry, Rigid Motions, and Patterns. COMAP.Arlington, Va.

1992 – Symmetry in the Aborignal Art of Australia. Symmetry: Culture and Science 3:227-240.

1994 – Tongan Symmetries. Proceedings of the Science of Pacific Island Peoples Conference, Suva. Vol.4:79-106.

2001 – Symmetries of Culture. In Bridges 2001: Mathematical Connections in Art, Music and Science. Conference proceedings. R. Sarhangi and S. Jablan, eds. Pp. 1-20. Southwestern College, Winfield, Kansas. Also available in the online journal Visual Mathematics 3 (2), http://members.tripod.com/vismath6/crowe1/index.html (accessed February 2, 2003).

Crowe, Donald W and Dénes Nagy

1992 – Cakaudrove-style Masi Kesa of Fiji. Ars Textrina 18:119-155.

Crowe, Donald W and Robin Torrence

1993 – Admiralty Islands Spear Decorations: A Minicatalogue of pmm Patterns. Symmetry: Culture and Science 4: 385-396.

Deregowski, J,B., P. McGeorge and V.Wynn

2000 – The role of Left-Right Symmetry in the Encodement of Spatial Orientations. British Journal of Psychology 91:241-257.

Eco, Umberto

1986 - Art and Beauty in the Middle Ages. New Haven: Yale University Press

1997 – Kant and the Platypus. New York: Harcourt Brace.

Elkins, James

1998 - On Pictures and the Words that Fail Them. Cambridge: Cambridge University Press.

Emmer, Michele

1993 – Visual Mind: Art and Mathematics. Cambridge: MIT Press.

Ewins, Rod

2004 – Symmetry and Semiotics: The Case of Fijian Barkcloth Figuration. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz: Amerind Foundation and Albuquerque: University of New Mexico Press.

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1992 - Symmetry in Chaos: A search for Pattern in Mathematics, Art and Nature. Oxford: Oxford University Press.

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1986 – The visual images of Fabric Structures in Ancient Peruvian Art. In The Junius B. Bird Conference on Andean Textiles. Pp. 47-80. The Textile Museum, Washington, D.C.

1991 – Structure, Image and Abstraction: Paracas Necropolis Headbands as System Templates. In Paracas Art and Architecture: Object and Context in South Coastal Peru. Anne Paul, ed. Pp. 110-171. Iowa City: University of Iowa Press.

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2004 – Jazz: An Andean Sense of Symmetry. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz: Amerind Foundation and Albuquerque: University of New Mexico Press.

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1970 – Design Structure and Social Interaction: Archaeological Implications of Ethnographic Analysts. American Antiquity 35:332-343.

Gerdes, Paulus

1989 – Reconstruction and Extension of Lost Symmetries: Examples from the Tamil of South India. In Symmetry 2: Unifying Human Understanding. Istvan Hargittai, ed. Pp. 791-813. Oxford: Pergamon Press.

1991 – Lusona: Geometrical Recreations of Africa. Higher Pedagogical Institute, Maputo, Mozambique.

1992 – African Pythagoras: A study in Culture and Mathematics Education. Higher Pedagogical Institute, Maputo, Mozambique.

1995 – Une tradition géometrique en Afrique – les dessins sur le sable. Paris: L’Harmattan.

1996 – Lunda Geometry: Designs, Polyominoes, Patterns, Symmetries. Higher Pedagogical Institute, Maputo, Mozambique.

1998 – Women, Art and Geometry in Southern Africa. Trenton, N.J: Africa World Press.

1999 – Geometry from Africa: Mathematical and Educational Explorations. Washington D.C. The Mathematical Association of America.

2000 – Le Cercle et le Carré. Créativité Géométrique, Artistique et Symbolique de Vannières et Vanniers d’Afrique, d’Amerique, d’Asie et d’Océanie. Paris: L’Harmattan.

2002a – Symmetrical Explorations Inspired by the Study of African Culture Activities. In Symmetry 2000, Part 1. Istvan Hargittai and T.C. Laurent, eds. Pp 75-89. London: Portand Press.

2002b – From Liki-Designs to Cycle Matrices: The Discovery of Attractive New Symmetries. Visual Mathematics 4 (1). Online journal at http://members.tripod.com/vismath7/gerd/index.html (accessed February 2, 2003).

Gerdes, Paulus and Gildo Bulafo

1994 – Sipatsi: Technology, Art and Geometry in Inhambane. Higher Pedagogical Institute, Maputo, Mozambique.

Grammer, Karl, and Randy Thornhill

1994 – Human (Homo Sapiens) Facial Attractiveness and Sexual Selection: The Role of Symmetry and Averageness. Journal of Comparative Psychology 108:233-242.

Grünbaum, Branko

1990 – Periodic Ornamentation of the Fabric Plane: Lessons from Peruvian Fabrics. Symmetry 1 (1):45-68. (Reprinted in this volume.)

2002 - Levels of Orderliness: Global and Local Symmetry. In Symmetry 2000, Part 1. Istvan Hargittai and T.C. Laurent, eds. Pp. 51-61. London: Portland Press.

Grünbaum, Branko and G.C.Shephard

1987 – Tilings and Patterns. San Francisco: Freeman.

Haake, A.

1989 – The Role of Symmetry in Javanese Batik Patterns. In Symmetry 2: Unifying Human Understanding, Istvan Hargittai, ed. Pp. 815- 826. Oxford: Pergamon Press.

Hahn, W.

1995 – Symmetry as a Developmental Principle in Nature and Art. Singapore: World Scientific.

Hanson, F. Allan

2004 – Symmetry for Itself, for Culture and for Practice. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz.: Amerind Foundation and Albuquerque: University of New Mexico Press.

Hardin, Margaret A., and Barbara J. Mills

2000 – Social and Historical Context of Short Term Stylistic Replacement: A Zuni Case Study. Journal of Archaeological Method and Theory 7: 139-163.

Hardonk, Marius Machiel

1999 – Cross-Cultural Universals of Aesthetic Appreciation in Decorative Band Patterns. 2 vols, Nijmegen, Netherlands: Nijmegen Institute for Cognition and Information.

Hargittai, Istvan

1991 – Fivefold Symmetry: Singapore: World Scientific.

Hargittai, Istvan, ed.

1989 – Symmetry 2: Unifying Human Understanding. New York: Pergamon Press. Also published in Computers and Mathematics with Applications 17 (1-6), 1989.

Hargittai, Istvan and Magdolna Hargittai

1994 – Symmetry: A Unifying Concept. Bolinas, Calif: Shelter Publications.

Hargittai, Istvan, and T.C.Laurent, eds.

2002 – Symmetry 2000, Parts 1 and 2. Wenner-Gren International Series, vol.80. London: Portland Press.

Hawryshyn, Craig W.

1992 – Polarisation Vision in Fish. American Scientist 80: 164-175.

Hays – Gilpin, Kelley Ann, Ann Cordy Deegan and Elizabeth Ann Morris

1998 Prehistoric Sandals from Northeastern Arizona. Anthropological Papers of the University of Arizona, no.62. Tucson: University of Arizona Press.

Hegmon, Michelle

1996 – The Social Dynamics of Pottery Style in the Early Puebloan South-West. Occasional Paper no.5, Crow Canyon Archaeological Center. Cortez, Colorado.

Humphrey, Diane

1997 – Preferences in Symmetries and Symmetries in Drawing: Asymmetries between Ages and Sexes. Empirical Studies of the Arts 15:41-60.

2004 – Symmetries in Development: The Eye is Quicker than the Hand. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz: Amerind Foundation and Albuquerque: University of New Mexico Press.

Humphrey, G. Keith and Diane E. Humphrey

1989 – Role of Structure in Infant Visual Pattern Perception. Canadian Journal of Psychology 43: 165-182.

Jablan, Slavik

1989 – Geometry in the Pre-scientific Period. History of Mathematical and Mechanical Sciences, Book 3. Mathematical Institute, Belgrade.

1997 – Theory of Symmetry and Ornament. Mathematical Institute, Belgrade. Also available online at: http://members.tripod.com/~modularity/mon.htm (accessed February 2, 2003).

2000 – Symmetry and Ornament. In Bridges 2000: Mathematical Connections in Art, Music and Science. Conference Proceedings. R.Sarhangi, ed. Pp. 1-12. Southwestern College, Winfield, Kansas.

2001 – Mirror Curves. In Bridges 2001. Mathematical: Connections in Art. Music and Science. Conference Proceedings. R. Sarhangi and S.Jablan, eds. Pp.233-246. Southwestern College, Winfield, Kansas. In modified form in the online journal Visual Mathematics 3 (2), http://www.mi.sanu.ac.yu/vismath/mir/index.html (accessed May 2, 2003).

2002 – Symmetry, Ornament and Modularity (expanded version of Jablan 1997). New Jersey, London, Singapore, Hong Kong: World Scientific.

Jolles, Frank

1993 – Zulu Beadwork as a Record of Historical Events: Some Theoretical Considerations. In Democratising Art and Art/Architectural History in South Africa. Proceedings from the Ninth Annual Conference of the South African Association of Art Historians. V. Mackenney, ed. Pp. 60-78. Durban, South Africa.

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1998 – Classification of One-Colour and Two-Colour Rosette Patterns. Leonardo 31:125-132.

Kappraff, Jay

1990 – Connections: The Geometric Bridge between Art and Science. New York: McGraw-Hill.

Kelly, Richard

1997 – Symmetry and the Combinable Natures of Printers’ Flowers. Journal of the Printing Historical Society 26:33-46.

Kessler, H.I.

1988 – Reading Ancient and Medieval Art. Word and Image 5 (1) (special whole issue).

Kowner, Rotem

1994 – Facial Asymmetry and Attractiveness Judgement in Developmental Perspective. Journal of Experimental Psychology: Human Perception and Performance 22:662-675.

Kubovy, Michael

1994 – Perceptual Organisation of Dot Lattices. Psychonomic Bulletin and review1:182-190

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2002 – Grouping by Proximity and Multi-stability in Dot Lattices: A Quantitative Gestalt Theory: Psychological Science 6:225-234.

Kubovy, Michael and Lars Strother

2004 – The Perception of Band Patterns: Going beyond Geometry. In Embedded Symmetries, Dorothy Washburn, ed. Dragoon, Ariz.: Amerind Foundation and Albuquerque: University of New Mexico Press.

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1989 – Perceptual Value of Symmetry. In Symmetry 2: Unifying Human Understanding. Istvan Hargittai, ed. Pp. 475-484. Oxford: Pergamon Press.

1992 – Symmetry Catches the Eye. In Eye Movements: From Physiology to Cognition. J.K.O’Regan and A.Levy-Schoen, eds.Pp.353-361. New York: Elsevier.

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1992 – The Influence of Stimulus Dimensionality and Viewing Orientation on Detection of Symmetry in Dot Patterns. Bulletin of the Psychonomic Society 30:43-46.

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1993 – Effects of Element Type and Spatial Grouping on Symmetry Detection. Perception. 22:565-587.

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1958 – The Gothic Image: Religious Art in France of the Thirteenth Century. New York: Harper and Row.

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1986 – Crystallographic Patterns. In Symmetry: Unifying Human Understanding. Istvan Hargittai, ed. Pp. 511-529. New York: Pergamon Press.

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1995 – Fluctuating Asymmetry and Body Weight in Men and Women: Implications for Sexual Selection. Ethology and Sociobiology 16: 145-153.

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1976 – Pottery Style and Society in Ancient Peru. Berkeley: University of California Press.

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2002 – Symmetry as a Quality Indicator of Individuals: Examples from Studies of Animal Welfare, Disease and Sexual Selection. In Symmetry 2000, Part 2. Istvan Hargittai and T.C. Laurent, eds. Pp. 409-418. London: Portland Press.

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1994 – Pattern and Space Perception in Young Infants. Spatial Vision 8: 141-165.

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1993 – Multicultural Mathematics. Oxford: Oxford University Press.

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2001 – Antisymmetry and Modularity in Ornamental Art. In Bridges 2001: Mathematical Connections in Art, Music and Science. Conference Proceedings. R Sarhangi and S. Jablan, eds. Pp. 55-66. Southwestern College, Winfield, Kansas.

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1982 – The Grammatical Study of Art Styles. Office of Computer Based Instruction, University of Delaware, Newark.

2004 – The Ghost in the Machine: Symmetry and Representation in Ancient Antillean Art. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz: Amerind Foundation and Albuquerque: University of New Mexico Press.

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1981 – Detection of Symmetry. Journal of Experimental Psychology: Human Perception and Performance 7:1186-1210.

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2001 – Bridges 2001: Mathematical Connections in Art, Music and Science. Conference Proceedings. Southwestern College, Winfield, Kansas.

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1990 – Visions of Symmetry: Notebooks, Periodic Drawings and Related Works of M.C.Escher. New York: W.H. Freeman.

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1948 – The Symmetry of Abstract Design with Special Reference to Ceramic Decoration. Contributions to American Anthroplogy and History, no.47. Washington D.C: Carnegie Institution.

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1980 – Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions, Cambridge: MIT Press.

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1995 – Fearful Symmetry: Is God a Geometer? Oxford, U.K.: Blackwell.

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1993 – Human Facial Beauty. Human Nature 4:237-269

1994 – Human Fluctuating Asymmetry and Sexual Behaviour. Psychological Science 5:297-302.

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1994 – Importance of Symmetry and Virtual Views in Three-Dimensional Object Recognition. Current Biology 4:18-23.

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1996 – Detection of Visual Symmetries. In Human Symmetry Perception. C.W.Tyler, ed. Pp 25-48. Also published in Spatial Vision (1995) 9:9-32.

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1983a Toward a Theory of Structural Style in Art. In Structure and Cognition in Art. Dorothy Washburn, ed. Pp. 138-164. Cambridge: Cambridge University Press.

1983b – Symmetry Analysis of Ceramic Design: Two tests of the Method on Neolithic Material from Greece and the Aegean. In Structure and Cognition in Art. Dorothy Washburn, ed. Pp. 138-164. Cambridge: Cambridge University Press.

1984 – The Usefulness of Typological Analysis for Understanding Aspects of Southern Prehistory: Some Conflicting Returns from Design Analysis. In Regional Analysis of Prehistoric Ceramic Variation: Contemporary Studies of the Cibola Whitewares. A. Sullivan and J Hantman, eds. Pp. 120-134. Anthropological Research Papers, no. 31. Arizona State University, Tempe.

1986a – Symmetry Analysis of Yurok, Karok and Hupa Indian Basket Designs. Empirical Studies of the Arts 4:19-45.

1986b – Pattern Symmetry and Coloured Repetition in Cultural Contexts. In Symmetry: Unifying Human Understanding. Istvan Hargittai, ed. Pp. 767-781. New York: Pergamon Press.

1987 – The Neighbour Factor: Basket Designs in Northern and Central California. Journal of California and Great Basin Anthropology 9:146-173.

1989 – The Property of Symmetry and the Concept of Ethnic Style. In Archaeological Approaches to Cultural Identity. S. Shennan, ed. Pp. 157-173. London: Allen and Unwin.

1990 – Style, Classification and Ethnicity: Design Categories on Bakuba Raffia Cloth. Transactions 80 (3). Philadelphia: American Philosophical Society.

1995 – Perception, Geometry and style. In Style, Society and Person. C.Carr and J. Neitzel, eds. Pp 101-122. New York: Plenum Press.

1999 – Perceptual Anthropology.: The Cultural Salience of Symmetry. American Anthropologist 101:547-562.

2000 – An Interactive Test of Colour and Contour Perception by Artists and Non-Artists. Leonardo 33: 197-202.

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2004 – The Genesis of Realistic Images and Patterned Design. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz: Amerind Foundation and Albuquerque: University of New Mexico Press.

Wasburn, Dorothy K. and Donald W. Crowe

1988 – Symmetries of Culture: Theory and Practice of Plane Pattern Analysis. Seattle: University of Washington Press.

Washburn, Dorothy and Andrea Petitto

1991 – Southern Laotician Textiles: Relationships between Pattern Structure and Weaving Technology. Ars Textrina 15: 35-66.

1993 – An Ethnoarchaeological Perspective on Textile Categories of Identification and Function. Journal of Anthropological Archaeology 12: 150-172.

Wenderoth, Peter

1994 – The Salience of Vertical Symmetry. Perception 23: 221-236.

Witherspoon, Gary and Glen Paterson

1995 – Dynamic Symmetry and Holistic Asymmetry in Navajo and Western Art and Cosmology. New York: Peter Lang.

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1992 – On the Role of Symmetry in Visual Search. Psychological Science 3: 194-198.

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2004 – Evolutionary Developments in the Cognition of Symmetry. In Embedded Symmetries. Dorothy Washburn, ed. Dragoon, Ariz: Amerind Foundation and Albuquerque: University of New Mexico Press.

Zaslavsky, Claudia

1999 – Africa Counts: Number and Pattern in African Culture. 3^rd ed. Chicago: Lawrence Hill Books.