Chaos and Economics


Published in 2000; updated on July 28, 2014.


Please note: Best viewed at 1280 x 1024 resolution.
Texts in blue italics are "
Texts in blue underline are links.
Texts with
N signify new or updated text.
Texts in black on white background are my texts, including My Fragments (MF#).
You are allowed to copy from my texts or pictures, providing the copyright is properly attributed to: ©Ben Tamari


Chaos Quotes

Johann Wolfgang von Goethe (1749-1832): "Conversations of Goethe with Eckermann and Soret;" Thursday, February 24, 1831.

"The difficulty in nature, is to see the law where it is concealed from us, and not to be misled by phenomena which contradict our senses."

In Lanker, B. (1989) "I Dream a World: Portraits of Black Women Who Changed America." Stewart, Tabori Chang, NY, p. 164.

Septima Clark: "I have great belief in the fact that whenever there is chaos, it creates wonderful thinking. I consider chaos a gift."






N My Fragments - From my personal point of view

For the complete list, please see Tamari .


MF17:     Our words are the clothes for our soul and our clothes are the words of our body.   Added 10 August 2010.


MF21:    Give me a nail and I will hang my God. (In the spirit of Archimedes.)    Added 1 August 2013.


MF22:    When the money illusion stops, the Gresham Law starts to operate.    Added 28 July 2014.






To those interested in this website:

This website is directed at people who are interested in dynamic systems in everyday life, especially with regard to economics. Most of the material written in this website is innovative and original. The approach here is entirely personal and NOT academic; you are invited to read it and judge for yourselves.

Many of you will understand a small fraction of the website's content, and a few will understand a great deal, but the website is meant to interest a wide range of people. Those lacking the relevant education will get something out of the photos and graphs that speak for themselves. Those with the relevant education will enjoy the content, which is straightforward and yet quite abstract and challenging.

For example, the Tamari Attractor is a system of equations that, the author believes, describes the economy of every country. It is possible, using this system of equations, to analyze each nation's own specific parameters and predict its economy, and compare one state’s economy to another’s on the same basis.

The website is written in a condensed manner, introducing only what is essential. Readers who wish to delve deeper into these subjects may refer to the many relevant books and links presented in the website, or use Google, Britannica or Wikipedia.

The website consists of ten pages. The first page (home) is introductory; the last page introduces the author. The remaining eight pages deal with various subjects in the two categories of chaos and economics. Each page functions as a separate, stand-alone unit, and presents the author's contribution to the subject. Since the content of this website is basically theoretical, it has been made as simple and user-friendly as possible.


The eight pages:


Tamari attractor  The Attractors page shows the main attractors in chaos literature (from an empirical point of view), including the Tamari attractor.

fractal tree  The Dreams page presents the human body, the head and brain, and also discusses dreams from the fractalization point of view.

Kepler Poligons  The Metaphors page shows the importance of mental pictures in creating new ideas.

pattern The Patterns page shows patterns and phenomena of fractals in nature.



The Nest  The Ecometry page presents the writings of Ben Tamari, and his method of analyzing and forecasting countries’ economies.

economic cycles  The Cycles page relates to economic/trade/business cycles, through only empiric findings.

Eco software The Economic Simulator enables the study of a country’s economy using the Eco software program.

Stocks Cycles The Stocks page introduces speculative cycles, which are empirically present in stock markets.







Chaos theory is a popular name for the theory of Dynamical Systems (DS), mainly in non-linear systems. (Scientifically, a chaotic DS is characterized by sensitivity to initial conditions. This sensitivity allows only for short-term forecasts and no more – such as predicting the weather, even though we are dealing here with deterministic systems that are describable through mathematical equations. As such, they should appear as orderly systems but actually appear to lack order; i.e., as being chaotic.) The theory covers many aspects of the life of DSs. They all share the same characteristics of being born, living and dying.







Auyang, T.S. (1998). "Foundations of Complex-System Theories in Economics, Evolutionary Biology, and Statistical Physics." Cambridge: Cambridge University Press.

Bak, P. (1997). "How Nature Works: The science of self-organized criticality." Cambridge: Cambridge University Press, p. 31.

Banks, J., Dragan V. and Jones A. (2003). "Chaos: A Mathematical Introduction." Cambridge: Cambridge University Press.

Burger, E.B. and Starbird M. (2005). "Coincidences, Chaos, and All That Math Jazz." New York: W.W. Norton Company, .

Chapman, R. and J.C. Sprott  (2005). "Images of a Complex World." Including CD, World Scientific.

Capra, F. (1996). "The Web of Life." New York: Anchor Books.

Ching-Yao, Hsieh and Ye Meng-Hua (1991). "Economics, Philosophy and Physics." New York: ME Sharpe.

Darvas, G. (2007). "Symmetry." Basel: Birkhouser.

Edwin, A.A. (1884). "Flatland." Princeton: Princeton University Press 1991.

Feder, J. (1988). "Fractals." New York: Plenum Press.

Frame, and Mandelbrot, Eds. (2002). "Fractals, Graphics, and Mathematics Education." The Mathematical Association of America.

Gleick, J. (1987). "CHAOS - Making a New Science." New York: Viking.

Gleick, and Porter (1990). "Nature's Chaos." New York: Little, Brown and Company.

Hall, N. (Ed.) (1991). "Exploring CHAOS." New York: W.W. Norton and Company.

Hilborn, R.C. (1994). "Chaos and Nonlinear Dynamics." Oxford: Oxford University Press.

Holden, A.V. (Ed.) (1986). "Chaos." Princeton: Princeton University Press.

Kauffman, S.A. (1993). "The Origins Of Order." Oxford: Oxford University Press.

Kelsey, D. (1988). "The Economics of Chaos Or the Chaos of Economics." Oxford University Press: Oxford Economic Papers 40.

Lesmoir-Gordon, N. (2004). "The Colours of Infinity: The Beauty, The Power and the Sense of Fractals." Inc. CD: Clear Books.

Levin J. (2002). "How The Universe Got Its Spots." Anchor Books  New York.

Lorenz, Edward N. (1993). "The Essence of Chaos." Washington DC: University of Washington Press.

McCouley, J.L. (1993). "Chaos, Dynamics, and Fractals." Cambridge: Cambridge University Press.

Marks-Tarlow, Terry (2008). " Psyche's Veil: Psychotherapy, fractals and complexity." London: Routledge.

Mira, C. (1987). "Chaotic Dynamics." World Scientific.

Mirowski, P. (1989). "More Heat Than Light: Economics as Social Physics, Physics as Nature's Economics." Cambridge: Cambridge University Press.

Moon, F.C. (1987). "Chaotic Vibrations." New York: John Wiley & Sons.

Ott, E. (1993). "Chaos in Dynamical Systems." Cambridge: Cambridge University Press.

Pickover, C.A. (1990). "Computers, Pattern, Chaos and Beauty." New York: St. Martin's Press.

Pickover, C.A. (1999). "Surfing Through Hyperspace." Oxford: Oxford University Press.

Prigogine, I. (1980). "From Being to Becoming." New York: W. H. Freeman and Company.

Reichl, L.E. (1992). "The Transition to Chaos." New York: Springer-Verlag.

Rucker, R. (1977). "Geometry, Relativity and the Fourth Dimension." Mineola: Dover.

Sardar, Z. and I. Abrams (1998). "Introducing Chaos." Cambridge: Icon Books.

Schroeder, M. (1991). "Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise." New York: W. H. Freeman and Company.

Seydel, R. (1988). "From Equilibrium To Chaos." New York: Elsevier.

Shaw, W.T. (2006). "Complex Analysis with MATHEMATICA®." Cambridge: Cambridge University Press.

Sornette, D. (2006). "Critical Phenomena in Natural Sciences." 2nd ed., Springer.

Tvede, L. (2006). "Business Cycles." 3rd ed. Chichester: John Wiley & Sons, Ltd.

Ward, M. (2001). "Universality, The Underlying Theory behind Life, the Universality and Everything." London: MacMillan.

Weeks, J.R. (2002). "The Shape of Space." 2nd ed.  New  York: Marcel Dekker, Inc.

Wegner, T. and B. Tyler (1993). "Fractal Creations." 2nd ed, Corte Madera: Waite Group Press.

Wiener, N. (1954). " The Human Use of Human Beings." Boston: Da Capo Press.

Zaslavsky, G.M. (1985). "Chaos in Dynamic Systems." Translated from Russian by V.I. Kisin, New York: Harwood AP.







Index sites







Science (Gleick) (Wolfram)