R. J. Moore and M. J. Ostwald, "Charting The Occurrence Of Nonlinear Dynamical Systems In Architecture," Architectural Science: Past Present and Future ed. S. Hayman, (Sydney: University of Sydney, 1993), pp. 223-235.
G. Deleuze and F. Guattari, A Thousand Plateaus. Capitalism And Schizophrenia trans. B. Massumi, (Minneapolis: University of Minnesota Press, 1987).
B. Massumi, A User's Guide To Capitalism And Schizophrenia: Deviations From Deleuze And Guattari (Cambridge, Massachusetts: M.I.T. Press, 1992).
For example Bloomer skirts around the question of relationships between nonlinearity and the works of Derrida on a number of occasions in Architecture and the Text: The(S)crypts of Joyce and Piranesi; especially links arising from the work of Hofstadter, Hayles, Deleuze and Guattari which allude to possible connections between Derrida and nonlinearity. See J. Bloomer, Architecture And The Text: The (S)crypts Of Joyce And Piranesi (New Haven: Yale University Press, 1993); N. K. Hayles, Chaos Bound: Orderly Disorder In Contemporary Literature And Science (Ithaca: Cornell University Press, 1990); Chaos And Order: Complex Dynamics In Literature And Science ed. N. K. Hayles, (Chicago: University of Chicago Press, 1991).
See Sorkin on Coop Himmelblau: M. Sorkin, Exquisite Corpse: Writings On Buildings (New York: Verso, 1991), pp. 346-347.
T. Mayne, Morphosis: Connected Isolation (London: Academy Additions, 1992), Architectural Monographs, n. 23, pp. 12-13.
K. Shinohara, "Chaos And Machine," Japan Architect (1988), v. 63, n. 5 (373), pp. 25-32.
R. J. Moore and M. J. Ostwald, "Icons Of Nonlinearity In Architecture: Correa - Eisenman - Van Eyck," Theatres of Decolonization (Arizona: University of Arizona Press, 1995), forthcoming.
R. R. Shearer, "Chaos Theory And Fractal Geometry: Their Potential Impact On The Future Of Art," Leonardo (1992), v. 25, n. 2, p. 143.
H. J. McWhinnie, "Chaos Theory: Some Questions Of Symmetry And Randomness In Art And Design IV," Design Methods: Theories, Research, Education (1993), v. 27, n. 2.
B. Hendersonsellers and D. Cooper, "Has Classical Music A Fractal Nature - A Reanalysis," Computers And The Humanities (1993), v. 27, n. 4, pp. 277-284.
M. V. Heuvel, "The Politics Of The Paradigm, A Case Study In Chaos Theory," New Theatre Quarterly (1993), v. 9, n. 35, pp. 255-266.
M. Berube and "Chaos And Order - Complex Dynamics In Literature And Science," American Literature (1993), v. 65, n. 3, pp. 596-598.
I. K. McEwan, "Instrumentality And The Organic Assistance Of Looms," Chora 1: Intervals In The Philosophy Of Architecture eds. A. Perez-Gomez and S. Parcell, (Montreal: McGill and Queens University Press, 1994), pp. 123-142.
M. Wigley, The Architecture of Deconstruction: Derrida's Haunt (Cambridge, Massachusetts: M.I.T. Press, 1993), p. 2-3.
C. T. Ingraham, "The Burdens Of Linearity," Strategies Of Architectural Thinking eds. J. Whiteman, J. Kipnis and R. Burdett, (Cambridge, Massachusetts: M.I.T. Press, 1992).
Wigley, The Architecture of Deconstruction p. xiii.
I. K. McEwan, Socrates' Ancestor: An Essay On Architectural Beginnings (Cambridge, Massachusetts: M.I.T. Press, 1993)
J. J. Rousseau, The People Of The Ideal Commonwealth And Their Expression Of Their General Will reprinted from A Treatise On The Social Compact: Or The Principles Of Politic Law (London: Becket, 1764), p. 69 in French Utopias: An Anthology Of Ideal Societies eds. F. E. Manuel and F. P. Manuel, (London: Collier-Macmillan Limited, 1966), p. 119.
J. Kipnis, "Drawing A Conclusion," Perspecta (1986), n. 22, p. 98.
D. Hollier, Against Architecture: The Writings Of Georges Bataille trans. B. Wing, (Cambridge, Massachusetts: M.I.T. Press, 1989).
J. Rajchman, "Weakness, Technologies, Events (An Introduction)," Columbia Documents Of Architecture And Theory: D (1992), v. 1, p. 161.
B. Tschumi, in C. T. Ingraham, J. Rajchman, and B. Tschumi, "Afterwords: Architecture And Theory Conference," Columbia Documents Of Architecture And Theory: D. (1992), v. 1, p. 169.
J. Derrida and M. Wigley, "Jacques Derrida: Invitation To A Discussion," Columbia Documents Of Architecture And Theory: D (1992), v. 1, p. 13.
C. T. Ingraham, in C. T. Ingraham, J. Rajchman, and B. Tschumi, "Afterwords," p. 169.
S. Agacinsk, "Shares Of Invention," Columbia Documents Of Architecture And Theory: D (1992), v. 1, p. 55.
Agacinsk, "Shares Of Invention," p. 56.
C. T. Ingraham, "Moving Target," Columbia Documents Of Architecture And Theory: D (1993), v. 2, p. 113. It is curiously fitting for this paper that Ingraham chooses the illustration, Sensitive Chaos (from Theodor Schwenk, Sensitive Chaos: The Creation of Flowing Forms in Water & Air, trans. Olive Whicher and Johanna Wrigley (New York: Schocken Books, 1976), to illustrate her paper.
Ingraham, "Moving Target," p. 114.
Ingraham, "Moving Target," p. 120.
Wigley, The Architecture of Deconstruction p. 16.
M. Wigley and J. Kipnis, "The Architectural Displacement of Philosophy," Pratt Journal Of Architecture ed. S. Perrella, (Spring 1988),v. 2, p. 8.
M. J. Ostwald and R. J. Moore, Exploring The Pedagogical Dimension Of Dwelling: Architecture As The Mathematical Unknown. (Working Paper: Newcastle University, 1996).
Derrida and Wigley, "Jacques Derrida: Invitation To A Discussion," p. 16.
Ingraham, "Moving Target," p. 113.
Prior to Gšdel's theorem all mathematics was assumed to be solvable - those few areas of continuing uncertainty were described as mathematical 'monsters' and attempts were made to classify them outside of mathematics. The mathematician Hilbert's final attempt to do this in the early twentieth century resulted in the creation of a first order language of mathematics in an effort to avoid the instability of self referentiality. It is this very instability which eventually lead to Gšdel's theorem. K. Gšdel, "Uber Formal Unentscheidbare Satze Der Principia Mathematica Und Verwandter Systeme 1," Monatschefte fur Mathematik und Physik (1931), n. 38. p. 173-198; D. Hofstadter, Gšdel, Escher Bach. An Eternal Golden Braid. (New York: Basic Books, 1979).
M. Barnsley, Fractals Everywhere (New York: Academic Press and Harcourt Brace Jovanovich, 1988), p. 187.
B. Mandelbrot, The Fractal Geometry Of Nature (New York: W. H. Freeman, 1983), p. 82.
Mandelbrot, The Fractal Geometry Of Nature p. 285.
Barnsley, Fractals Everywhere p. 109.
Barnsley, Fractals Everywhere p. 107.
See Derrida's analysis of naming of C. Lévi-Strauss' Tristes Tropiques trans. J. Weightman and D. Weightman, (London: Jonathon Cape, 1973); J. Derrida Of Grammatology trans. G. C.Spivak, (Baltimore: The Johns Hopkins University Press, 1976).
Wigley, The Architecture of Deconstruction p. 8.
Mandelbrot, The Fractal Geometry Of Nature p. C2.
Wigley, The Architecture of Deconstruction p. 12-13.
Barnsley, Fractals Everywhere p. 1, emphasis added.
H. W. Franke, "Refractions of Science into Art," The Beauty Of Fractals eds. H. O. Peitgen and P. Richter, (New York: Springer-Verlag, 1986), p. 181, emphasis added.
G. Eilenberger, "Freedom, Science, and Aesthetics," The Beauty Of Fractals eds. H. O. Peitgen and P. Richter, (New York: Springer-Verlag, 1986), p. 175.
Eilenberger, "Freedom, Science, and Aesthetics," p. 175.
Barnsley, Fractals Everywhere p. 208.
Barnsley, Fractals Everywhere p. 172-173.
Mandelbrot and Schroeder; exceptions to this general observation are discussed later in this paper.
Mandelbrot, The Fractal Geometry Of Nature p. 131-132.
H. Hahn, "The Crisis in Intuition," The World Of Mathematics ed. J. Newman, (New York: R.Simon and Schuster, 1956) v. 3.
Mandelbrot, The Fractal Geometry Of Nature p. 131-132.
M. Schroeder, Fractals, Chaos, Power Laws. Minutes From An Infinite Paradise (New York: W. H. Freeman, 1991) p. 19-20.
Schroeder, Fractals, Chaos, Power Laws p. 84.
Schroeder, Fractals, Chaos, Power Laws p. 84.
Schroeder, Fractals, Chaos, Power Laws p. 69.
Schroeder, Fractals, Chaos, Power Laws p. 69.
A view supported without resorting to architectural metaphors by; A. McRobie and M. Thompson, "Chaos, Catastropies And Engineering," The New Scientist Guide To Chaos ed. N. Hall, (London: Penguin Books, 1992), p. 149-161.
Schroeder, Fractals, Chaos, Power Laws p. 224.
Schroeder, Fractals, Chaos, Power Laws p. 225.
Wigley and Kipnis, "The Architectural Displacement of Philosophy," p. 98.
I. Stewart and M. Golubitsky, Fearful Symmetry: Is God A Geometer? (London: Penguin Books, 1992), p. 249.
Mandelbrot, The Fractal Geometry Of Nature p. 23-24.
Consider that the Miesian building is essentially rectilinear in plan. Rectilinear windows, doors and internal spaces divide the overall mass of the building into smaller rectangular zones. Upon further close examination the Miesian building is also composed of right-angled details, and rectangular structural members and cladding forms. The Miesian building, and its modernist progeny, are self similar at up to ten obvious levels of scaling - far more than the Castel del Monte!
It should be noted that in teaching scientific concepts two qualities are held in high regard. Firstly all scientific teaching is expected to be derived from logical assumptions, from experimentation and from careful observation. Secondly scientific writing, more so than in any other discipline, is expected to be without personal bias. Mandelbrot fails in both regards.
Mandelbrot, The Fractal Geometry Of Nature p. 23.
Barnsley, Fractals Everywhere p. 299.