Churning Madness

I somewhat recently read “The Colour of Infinity: The Beauty and Power of Fractals“; I studied Chaos and Fractals a bit back in MSSM, but in the past decade surely there has to have been advancements.

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.

Tags: Arthur C. Clarke, Benoît Mandelbrot, fractals, geometry, self-similarity, web

This entry was posted on Sunday, April 6th, 2008 at 16:04 and is filed under Books, Education, Geek-ness, Math, Nifty. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.