Shape

400 Notes to pp. 304–305
13. T. W. Knight, ‘‘Color Grammars: Designing with Lines and Colors,’’ Environment and Planning
B: Planning and Design 16 (1989): 417–449. See also N. Goodman, The Structure of Appearance (Indianapolis:
Bobbs-Merrill, 1966).
14. G. Stiny, ‘‘A Note on the Description of Designs,’’ Environment and Planning B 8 (1981): 257–
267. G. Stiny, ‘‘What is a Design?’’ Environment and Planning B: Planning and Design 17 (1990): 97–
103.
15. G. Stiny, ‘‘Shape Rules: Closure, Continuity, and Emergence,’’ Environment and Planning B:
Planning and Design 21 (1994): s49–s78. G. Stiny, ‘‘Useless Rules,’’ Environment and Planning B:
Planning and Design 23 (1996): 235–237. G. Stiny, ‘‘How to Calculate with Shapes,’’ 50–61.
16. S. C. Chase, ‘‘Modeling Designs with Shape Algebras and Formal Logic’’ (PhD dissertation,
University of California, Los Angeles, 1996). S. C. Chase, ‘‘Shape Grammars: From Mathematical
Model to Computer Implementation,’’ Environment and Planning B: Planning and Design 16 (1989):
215–242.
17. C. F. Earl, ‘‘Shape Boundaries,’’ Environment and Planning B: Planning and Design 24 (1997):
668–687. R. Krishnamurti and C. F. Earl, ‘‘Shape Recognition in Three Dimensions,’’ Environment
and Planning B: Planning and Design 19 (1992): 585–603. I. Jowers and C. F. Earl, ‘‘Classifying
Shape Algebras by Types of Elements and Space’’ (paper, The Open University, Milton Keynes,
U.K., 2005).
18. T. W. Knight, ‘‘Computing with Emergence,’’ Environment and Planning B: Planning and Design
30 (2003): 125–155. T. W. Knight, ‘‘Computing with Ambiguity,’’ Environment and Planning B:
Planning and Design 30 (2003): 165–180. For some history, see T. W. Knight, ‘‘either/or fi and,’’
Environment and Planning B: Planning and Design 30 (2003): 327–338, but also, with a complementary
slant, P. Galison, ‘‘Aufbau/Bauhaus: Logical Positivism and Architectural Modernism,’’ Critical
Inquiry 16 (1990): 709–752. Novel algebras and ways of calculating are always welcome, yet an
open invitation needn’t mean familiar algebras and ways of calculating are incomplete. I believe
many of Knight’s speculative proposals are also covered in the schemas I show in part III. Different
ways of doing the same thing are appealing in different ways. At least, there’s a chance for an algebraic
type of ambiguity.
19. R. Krishnamurti, ‘‘The Arithmetic of Shapes,’’ Environment and Planning B 7 (1980): 463–484.
R. Krishnamurti, ‘‘The Construction of Shapes,’’ Environment and Planning B 8 (1981): 5–40. R.
Krishnamurti, ‘‘The Maximal Representation of a Shape,’’ Environment and Planning B: Planning
and Design 19 (1992): 267–288. R. Krishnamurti, ‘‘The Arithmetic of Maximal Planes,’’ Environment
and Planning B: Planning and Design 19 (1992): 431–464.
20. D. Krstic, ‘‘Algebras and Grammars for Shapes and Their Boundaries,’’ Environment and Planning
B: Planning and Design 28 (2001): 151–162. D. Krstic, ‘‘Computing with Analyzed Shapes,’’
in Design Computing and Cognition ’04, ed. J. Gero (Dordrecht: Kluwer Academic, 2004), 397–
416.
21. L. March, ‘‘Babbage’s Miraculous Computation Revisited,’’ Environment and Planning B: Planning
and Design 23 (1996): 369–376.
22. M. A. Tapia, ‘‘From Shape to Style’’ (PhD dissertation, University of Toronto, 1996).
23. G. A. Miller, ‘‘Information Theory in Psychology,’’ in The Study of Information: Interdisciplinary
Messages, ed. F. Machlup and U. Mansfield (New York: John Wiley and Sons, 1983), 495–496.