The book at three sections, which are basically: old and broken way, new and shiny way, and finally a summary of points to take away from the book.

I’ve not economics or financial training, so the first chapter was quite educational, pretty much capturing the development of modern practiced financial theory. Along the way, he shows many of the assumptions and estimations that went into each step, and also alludes to studies that show these assumptions are not true.

The second section was also educational, in respect to fractal analysis that’ve been done to financial data. Along with many nifty details about fractals and probability distributions the basic results is to show that:

• price variations at any time-scale are Power Law distributed, not Gaussian distributed as theory assumes.
• price variations at any time-scale are time-dependant or Fractional Brownian Motion, not independent or traditional Brownian Motion as theory assumes.

It goes on to demonstrate a multi-fractional construction that seems to account for these factors. as well as “fractional time” to create a time series that manifests all known anomalous characteristics of market behaviour by traditional analysis.

The book has a rich history, and fascinating contradictions to what I was taught. However, it… wasn’t very moving at the end. It didn’t have a silver bullet. I know this is science, and science’s best discoveries are the new anomalies. Yet, I couldn’t help being disappointed. In a literary sense, this book had a “pathetic” ending.

Despite all the educational aspects, ground-breaking work discussed, I didn’t get as much from it as I had hoped. 2 of 4 possible stars.

The book is broken down into 8 Chapters: several are by popularizers of Fractals, several are republished papers by active researchers, and one covers the making of the educational video. This video and book was endorsed / promoted by the recently deceased Sir Arthur C. Clarke.

I found several chapters of note:

• Chapter 1: “The Nature of Fractal Geometry” is the intro written by Ian Stewart, a mathematician, professor, and prolific popularizer of science. Well written prose that targets laymen with an amateur interest in science and math.
• Chapter 3: “A Geometry Able to Include Mountains and Clouds” written by Benoît Mandelbrot, the central figure in the development of fractal geometry. His article derived from a lecture to a Nobel Conference in 1990, and covers many of the aspect of fractal geometry in more detail:
  • Clouds, mountains and coasts; self-similar natural systems, fractal dimensionality and roughness.
  • Seemingly infinite complexity arising from fundamentally simple transformations.
  • Most striking was the “diffusion limited aggregations (DLAs)”, which show the fractal nature of natural systems growing & evolving over time.
• Overall, I found this article compelling because of the holistic synthesis, and the obviously deep and finessed presentation Mandelbroit gives.
• Chapter 6: “Self-organization, Self-regulation, and Self-similarity on the Fractal Web” is written by Gary Willaim Flake and David M. Pennock, then at Yahoo! Research Labs. This paper addresses many related issues, including:
  • The positive feedback loops of authors, search engines, and readers through a page’s connectedness, its page rank, and its traffic, respectively.
  • The self similarity of network traffic, and the power law distribution of it.
  • Other web metrics which also obey power law distributions, such as inbound & outbound links.
  • Community structures that form into fairly regular bipartite relationships of hubs and authorities.

  Anyway, this paper by far proved the viability of fractal pattern analysis to a very new, vital and familiar technology.

• Chapter 7: “The Human Social Experience Forms a Social Fractal”, written by Robert R. Prechter, J., covers the concept that the financial markets are a fractal phenomena. The analysis given was simplistic, yet the concept was compelling. Thus I’ve picked up a book about that subject exactly to get a better feel… but that’s another post. Interesting concept; weak presentation.

The book also comes with a DVD containing the documentary video. It’s a very simplified intro to fractals, as in elementary / middle school usage. It’s not very detailed or thought provoking on a mathematical / scientific level. However, it’s meant to share the artistic wonder of a fractal, and it does a decent job there. My only lamentation is that the video was not remastered for DVD; there are obvious analog artifacts that distracted me from the intent of the visual experience. Additionally, I felt the Davoid Gilmour soundtrack was unnecessary / dated.

Overall, it was a good investment. 3 / 4 possible stars.