Hey folks. I’ve decided that the serialization of LWIA v3 is simply far too delayed, and that I’m going to get through it in a series of three omnibus posts so that it’s wrapped up before the 60th Anniversary Doctor Who Specials. Right now those are still set to be Patreon-exclusive, with roughly $370 a month to go before they happen on the site. You can help by backing my Patreon, where I’ve got reviews of the first five installments of Tales of the TARDIS up, with the last going up later today.
Previously in Last War in Albion: Alan Moore became fascinated by fractals, or at least by what he thought fractals were.
The blue world spins below me, fragile as glass, a vast and delicate ornament. Naked creation crackling and streaming off in all directions. Clouds are not spheres. Mountains are not cones. Lightning does not travel in a straight line. These things are abstractions of reality. The geometry of nature, like the geometry of life itself, contains infinites.” – Grant Morrison, Animal Man
Allow a moment of fancy. It will not escape notice that Dewdney’s introduction sounds very much like something Alan Moore might write, and thus almost tailor made to capture his eye. Could this article in fact have been his introduction to the Mandelbrot set? Certainly Moore was an avid reader of popular science magazines. He generally favored New Scientist, but it’s easy to imagine him passing by a newsstand and seen the striking visualization of the set on the cover, a crackling flame tongue in all its mad and infinite detail. If so, and if he picked up the issue out of curiosity, what would he have learned? Much of the article consisted of semi-technical explanations of complex numbers and computer programs that would have sailed over his head, but his eye would surely have been caught by the thrilled descriptions of how “the numbers inside remain to drift or dance about. Close to the boundary minutely choreogrphed wanderings mark the onset of the instability. Here is an infinite regress of detail that astonishes us with its variety, its complexity and its strange beauty,” or the lush descriptions of the recurring patterns within the set: “a riot of organic-looking tendrils and curlicues sweeps out in whorls and rows. Magnifying a curlicue reveals yet another scene: it is made up of pairs of whorls joined by bridges of filigree.” Ultimately, however, one suspects the key detail, beyond the breathtaking illustrations, would have been the subheadline billing the Mandelbrot set as “the most complex object in mathematics” would surely have been eye-catching. (Indeed, Moore parroted the line in an interview, describing the Mandelbrot set as “the most complex shape in mathematics, and possibly the most complex shape in the universe.”)
It is worth unpacking that complexity a little. In the case of the Koch snowflake, zooming in on the image generates the same pattern. Pick a single point to zoom in on and you’ll see an endlessly repeating jagged series of triangles.…