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,' a property called self-similarity." ( 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.