Sunday, October 17, 2010


Since the sub-title of this blog is "On fractal change", and since, as Jason Kottke notes, the inventor of the concept of the fractal, Benoit Mandelbrot, has died, I thought this might be a good moment to expand a little on what I mean by the word, and what the word means for me. First, here's Wikipedia's entry, and here's its initial definition, borrowed from Mandelbrot himself: "A fractal is 'a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,'[1] a property called self-similarity." ([1] The Fractal Geometry of Nature). Which may not be all that helpful by itself, but that last word, "self-similarity", is a clue to why the concept has spread so widely, to cover things like the shape of leaves or clouds or coastlines or financial charts or culture.

Mandelbrot gave the term a technical and mathematical meaning, but what I want is its metaphoric aspect. As a metaphor, "fractal" describes things in which similar, though never identical, patterns reappear at all scales large and small. And this can help in two ways: first, by providing a kind of handle or way of grasping the structure of systems that otherwise appear monolithic and either chaotic or complex; and second, by alerting us to the way in which patterns, whether spatial, temporal, or otherwise, can change in scale abruptly or discontinuously -- Mandelbrot's book on financial markets, for example, The (Mis)Behavior of Markets, was in many ways an early insight into the "black swan" phenomenon that Nassim Taleb has popularized. So, in speaking of "fractal change", I'm referring to historical patterns that repeat on scales varying from an individual's day to day job, to vast "phase changes" in the very structure of human societies. And I'm also referring to the way in which change can surprise us by sudden shifts in scale, as in a televised rant becoming the seed of an anomalous political movement.

But here, with a hat tip to Jason Kottke again, and in memory of Benoit Mandelbrot, is a journey into the infinite depths of the greatest fractal ever, the Mandelbrot Set:

Mandelbrot Fractal Set Trip To e214 HD from teamfresh on Vimeo.


  1. Holy iterations ratman.

    Fractals may work well in terms of describing snowflakes, leaves, or even mountain ranges. Some clever economists may use them to show market fluctuations, chaotic/unpredictable activity, etc. However, the fractal craze ...and chaos fetish tends to obfuscate matters- economically, scientifically, or otherwise. (the belgian physicist Bricmont has written some interesting things on this issue). People aren't snowflakes, morf.

    Many geeks crave chaos, "stochastics" and indeterminacy, even when it's not there. The market may look chaotic as a casino floor--but really the underlying economic activity (...labor, production, manufacturing, etc) is determined, and rather stable, at least in terms of humans working and having certain economic/biological requirements.

    The free market advocates want instability, really--day traders depend on volatility, probability/odds, great swings/shifts, as much as a person at a craps table does. But that's generally only to the benefit of the day trader. Not the populace at large.

    Economically speaking, indeterminacy tends to benefit the wealthy and powerful (and I believe that can be empirically verified)--much as the high roller who sits down at the poker table with a $1000 cleans up from the chumps who bought in for $50. Jerry Buss-o-nomics.

  2. No, J, I'm afraid that this time you're demonstrating an ignorance of basic probability. A person at a craps or poker table loses on average, and "high rollers" simply lose more on average -- that's what pays for the casinos.

    Free markets, on the other hand, are simply what the words mean -- people freely trading goods and services with one another. Which has inherently nothing to do with "indeterminacy", much less craps tables. Free markets have enormously benefited the populace at large.

  3. IM afraid you don't understand my point. The craps table example was merely an analogy. Even if over the long run a craps player will generally lose via odds, a high roller can afford it, and will often win big just via luck. Playing poker's another matter--the high roller nearly always wins because of leverage. And that's the same with market activity, stocks, speculation, regardless of yr usual apology for trickle down, "freedom", so forth. Walmart is not trading fairly with Ma n Pa's tire shoppe (or whatever shoppe). Wallymart arrives, and Ma n Pa shoppes are out of business in a few months, or weeks.

  4. Oh, I see -- so you think you can lose "via odds" but win big "via luck", hmm? You think somehow "luck" will magically overcome "odds"?

    Maybe it's not that I don't understand your point -- maybe it's that your "point" is ridiculous.

  5. Not exactly. And yes, people often win via gambler's luck, especially at pure chance games like craps. (Poker is not pure chance, but involves betting strategies--leverage). That's why it's called gambling. You simply don't know anything about economics, or gambling, or apparently probability for that matter.

    And if you can't see that Wallymart vs Ma n Pa shoppes is not freedom, then...res ipsa loquitur.

  6. Not exactly. And yes, ...

    Is "gambler's luck" different from "luck", J? Does it violate the laws of probability or odds? If so, here's how you too can become rich -- talk a few dozen fellow believers/idiots into pooling their money in a consortium, become a "high-roller" yourself thereby, and then split the proceeds after you win big via "gambler's luck"! Nothing to it!

  7. And if you can't see that Wallymart vs Ma n Pa shoppes is not freedom,...

    Forget the Ma n Pa shoppes, and just consider Ma and Pa -- or rather all the ma's and pa's and others who voluntarily shop at Wallymart because they benefit by it. And then consider the Wallymart competitors, from Target to small, customer-oriented boutiques, who cater to those looking for more than simple price-breaks. And then, in contrast, consider those who would like to be able to force people to shop where and how they think is best -- and yeah, res ipsa loquitur.

  8. It's you that's missing the point on probability--the odds of getting snake eyes may be only 1/36, but at times some vegas rogue puts down 10 grand and may hit it first time--thus defeating the supposed law of averages. But that's not a model for rational economics (but for some speculators/day traders it is). Humans don't want casino-economics. They want security--many would probably be out on a farm, than in an office. It's libertarians who insist that casino-capitalism is the best for all.

    AS far as Wallymart and supposed "choice"--consumers don't have much a choice once W-mart arrives. The rest of the shops are out of bidness, and the employees now wearing w-mart uniforms (or collecting welfare).

  9. It's libertarians who insist that casino-capitalism is the best for all.

    Ah, no, it's libertarians who insist that luck does not defeat the law of averages, and that casinos are no model for capitalism at all.

    AS far as Wallymart and supposed "choice"--consumers don't have much a choice once W-mart arrives. The rest of the shops are out of bidness,...

    Why would that be? Because Walmart holds a gun to their heads? Or because consumers actually want to shop at Walmart?


You can use some HTML tags, such as <b>, <i>, <a>