Finding Your Way Through Chaos,Fractals,and Other Exotic Mathematical Objects: a Guide for the Perplexed

Abraham, R. , & Shaw, C. ( 1992). Dynamics: The Geometry of Behavior. 2nd ed. Redwood City, CA: Addison-Wesley .

Antal, B. ( 2008). The fractal organization of transference, defense, and interpretation understood as temporal metaphors. Presentation, Society for Chaos Theory in Psychology and Life Sciences

Arrow, H. , Mcgrath, J.E. , & Berdahl, J.L. ( 2000). Small Groups as Complex Systems. Thousand Oaks, CA: Sage Publications.

Binder, P. ( 2008). Frustration in complexity. Science 320:322-323.

Bion, W. ( 1977). Seven Servants. New York: Aronson.

Boring, E. ( 1950). A History of Experimental Psychology. 2nd ed. New York: Appleton-Century-Crofts .

Coburn, W. ( 2000). The organizing forces of contemporary psychoanalysis: Reflections on nonlinear dynamic systems theory. Psychoanalytic Psychology 17:750-770.

Coburn, W. ( 2002). A world of systems: The role of systematic patterns of experience in the therapeutic process. Psychoanalytic Inquiry 22:655-677.

Coburn, W. ( 2007). Psychoanalytic complexity: Pouring new wine directly into one’s mouth. In New Developments in Self Psychology Practice, ed. P. Buirski & A. Kottler. Lanham, MD: Aronson, pp. 3-22.

Davis, S. ( 2002). The relevance of Gerald Edelman’s theory of neuronal group selection and nonlinear dynamic systems for psychoanalysis . Psychoanalytic Inquiry 22:814-840.

Devaney, R. , & Keen, L. ( 1989). Chaos and Fractals: The Mathematics behind the Computer Graphics. Providence, RI: American Mathematical Society.

Dijksterhuis, E. ( 1950). The Mechanization of the World Picture. London: Oxford University Press.

Edelman, G. ( 1987). Neural Darwinism: The Theory of Group Selection . New York: Basic Books.

Érdi, P. ( 2007). Complexity Explained. New York : Springer.

Freeman, W. ( 2000). How Brains Make up Their Minds. New York: Columbia University Press.

Freeman, W. ( 2007). A biological theory of brain function and its relevance to psychoanalysis. In Self-Organizing Complexity in Psychological Systems, ed. C. Piers , J. Muller , & J. Brent. Lanham, MD: Aronson, pp. 37-82.

Freud, S. ( 1914). On narcissism: An introduction. Standard Edition 14:67- 102.

Galatzer-Levy, R. ( 1995). Psychoanalysis and dynamical systems theory: Prediction and self similarity. Journal of the American Psychoanalytic Association 43:1085-1113.

Galatzer-Levy, R. ( 2002). Emergence. Psychoanalytic Inquiry 22:708-727.

Galatzer-Levy, R. ( 2004). Chaotic possibitilies: Toward a new model of development . International Journal of Psychoanalysis 85:419-441.

Galatzer-Levy, R. (in press). Good vibrations: Analytic process as coupled oscillators. International Journal of Psychoanalysis 90.

Gleick, J. ( 1987). Chaos: Making a New Science. New York : Viking.

Gordon, J. , Rucker, R. , & Walker, J. ( 1990). Chaos: The software. Sun Rafael, CA: Autodesk.

Gottman, J. , Murray, J. , Swanson, C. , Tyson, R. , & Swanson, K. ( 2002). The Mathematics of Marriage: Dynamic Nonlinear Models . Cambridge: MIT Press.

Gould, S.J. ( 1977). Ontongeny and Phylogeny. Cambridge : Harvard University Press.

Gros, C. ( 2008). Complex and Adaptive Dynamical Systems: A Primer . New York: Springer.

Guastello, S.J. ( 2002). Managing Emergent Phenomena: Nonlinear Dynamics in Work Organizations. Mahwah, NJ: Erlbaum .

Guastello, S.J. , Koopmans, M. , & Pincus, D. , EDS. ( 2009). Chaos and Complexity in Psychology: Theory of Nonlinear Dynamics. New York: Cambridge University Press.

Harris, A. ( 2005). Gender as Soft Assembly. Hillsdale, NJ: Analytic Press.

Harris, A. ( 2009). "You must remember this." Psychoanalytic Dialogues 19:2-21.

Hershberg, S. ( 2006). Pathways of growth in the mother-daughter relationship . Psychoanalytic Inquiry 26:56-69.

Holland, J. ( 1998). Emergence: From Chaos to Order. New York: Perseus.

Kauffman, S. ( 1993). The Origins of Order: Self-Organization and Selection in Evolution. New York: Oxford University Press.

Kohut, H. ( 1971). The Analysis of the Self. New York : International Universities Press.

Leffert, M. ( 2008). Complexity and postmodernism in contemporary theory of psychoanalytic change. Journal of the American Academy of Psychoanalysis & Dynamic Psychiatry 36:517-542.

Levin, C. ( 2006). "That’s not analytic": Theory pressure and "chaotic possibilities" in analytic training. Psychoanalytic Inquiry 26:767-783.

Levin, F. ( 2003). Psyche and Brain: The Biology of Talking Cures . Madison, CT: International Universities Press.

Levinson, E. ( 1994). The uses of disorder: Chaos theory and psychoanalysis . Contemporary Psychoanalysis 30:5-24.

Li, T.Y. , & Yorke, J.A. ( 1975). Period three implies chaos. American Mathematical Monthly 82:985-992.

Lorenz, E. ( 1993). The Essence of Chaos. Seattle : University of Washington Press.

Lyons-Ruth, K. ( 1999). The two-person unconscious: Intersubjective dialogue, enactive relational representation, and the emergence of new forms of relational organization. Psychoanalytic Inquiry 19:576-617.

Mandelbrot, B. ( 1982). The Fractal Geometry of Nature. San Francisco: Freeman.

Mandelbrot, B. ( 2001). Fractals in Science, Engineering, and Finance (Roughness and Beauty). MIT World. http://mitworld.mit.edu/video/52

May, R. ( 1976). Simple mathematical models with very complicated dynamics . Nature 261:459-467.

Moran, M. ( 1991). Chaos theory and psychoanalysis: The fluidic nature of the mind. International Review of Psychoanalysis 18:211-221.

NOVA(2008). Hunting the hidden dimension. PBS (online).

Palumbo, S. ( 1999). The Emergent Ego: Complexity and Coevolution in the Psychoanalytic Process. Madison CT: International Universities Press.

Palumbo, S. ( 2007). Complexity theory as the parent science of psychoanalysis . In Self-Organizing Complexity in Psychological Systems , ed. C. Piers , J. Muller , & J. Brent. Lanham, MD: Aronson, pp. 1-14.

Peitgen, H.-O. , Jürgens, H. , & Saupe, D. ( 2006). Chaos and Fractals: New Frontiers of Science. 2nd ed. New York: Springer .

Peitgen, H.-O. , & Richter, P. ( 1986). The Beauty of Fractals: Images of Complex Dynamical Systems . Berlin: Springer.

Piers, C. ( 2000). Character as self-organizing complexity. Psychoanalysis & Contemporary Thought 23:3-34.

Pincus, D. , Freeman, W.J. , & Modell, A. ( 2007). A neurobiological model of perception: Considerations for transference. Psychoanalytic Psychology 24:623-640.

Pincus, D. , & Guastello, S. ( 2005). Nonlinear dynamics and interpersonal correlates of verbal turn-taking patterns in a group therapy session. Small Group Research 36:635-677.

Priel, B. , & Schreiber, G. ( 1994). On psychoanalysis and non-linear dynamics: The paradigm of bifurcation. British Journal of Medical Psychology 67:209-218.

Procci, W. ( 2002). Chaos theory as a new paradigm in psychoanalysis: A contribution to the discussion of models. International Journal of Psychoanalysis 83:487-490.

Rubenfeld, S. ( 2001). Group therapy and complexity theory. International Journal of Group Psychotherapy 51:449-471.

Sawyer, W.W. ( 1961). What is Calculus About? New York: Random House.

Seligman, S. ( 2002). Louis Sander and contemporary psychoanalysis: An introduction . Psychoanalytic Dialogues 12:1-10.

Seligman, S. ( 2005). Dynamic systems theories as a metaframework for psychoanalysis . Psychoanalytic Dialogues 15:285-319.

Sprott, J.C. ( 1992). Sprott’s fractal gallery. Available online: http://sprott.physics.wisc.edu/fractals.htm

Sprott, J.C. ( 2003). Chaos and Times-Series Analysis. New York: Oxford University Press.

Sprott, J.C. ( 2009). Sprott’s gateway. Available online: http://sprott.physics.wisc.edu/

Sprott, J.C. , & Rowlands, G. ( 2009). Chaos Demonstration, Version 3 (computer software) . Raleigh, NC: Physics Academic Software.

Spruiell, V. ( 1993). Deterministic chaos and the sciences of complexity: Psychoanalysis in the midst of a general scientific revolution. Journal of the American Psychoanalytic Association 41:3-44.

Stein, A. ( 1999). Whose thoughts are they, anyway? Dimensionally exploding Bion’s "double-headed arrow" into coadapting, transitional space. Nonlinear Dynamics, Psychology, & Life Sciences 3:65-92.

Stern, D.N. , Sander, L.W. , Nahum, J.P. , Harrison, A.M. , Lyons-Ruth, K. , Morgan, A.C. , Bruschweiler-Stern, N. , & Tronick, E.Z. ( 1998) Noninterpretive mechanisms in psychoanalytic therapy: The ‘something more’ than interpretation. International Journal of Psychoanalysis 79:903-921.

Stewart, I. ( 2002). Does God Play Dice? 2nd ed. New York: Blackwell.

Stolorow, R. ( 1997). Dynamic, dyadic, intersubjective systems: An evolving paradigm for psychoanalysis. Psychoanalytic Psychology 14:337-346.

Strogatz, S. ( 1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Cambridge, MA: Westview.

Strogatz, S. ( 2003). Sync: The Emerging Science of Spontaneous Order . New York: Theia.

Taerk, G. ( 2002). Moments of spontaneity and surprise: The nonlinear road to something more. Psychoanalytic Inquiry 22:728-739.

Thelen, E. , & Smith, L. ( 1994). A Dynamic Systems Approach to the Development of Cognition and Action. Cambridge: MIT Press .

Thom, R. ( 1975). Structural Stability and Morphogenesis: An Outline of a General Theory of Models. Reading, MA: Benjamin.

Tyson, P. ( 2005). Affects, agency, and self-regulation: Complexity theory in the treatment of children with anxiety and disruptive behavior disorders . Journal of the American Psychoanalytic Association 53:159-187.

Wiener, N. ( 1956). I am a mathematician, the later life of a prodigy; an auto-biographical account of the mature years and career of Norbert Wiener and a continuation of the account of his childhood. In Ex-prodigy . Garden City, NY: Doubleday.

Wiener, N. ( 1961). Cybernetics: Or Control and Communication in the Animal and the Machine. 2nd ed. Cambridge : MIT press.

Wigner, E. ( 1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics 13:1-14.

Wolfram, S. ( 2002). A New Kind of Science. Champaign IL : Wolfram Media.

Zeeman, C. ( 1977). Catastrophe Theory: Selected Papers 1972-1977 . Reading, MA: Addison-Wesley .