Fractilic Landscapes

Yesterday afternoon I recorded an interview for KPFK’s Poet’s Cafe with Lois P. Jones, which will air in a couple months (obviously I’ll let you know when it’s scheduled). As I was sitting in the studio, babbling into the big padded mike about fractals for what seems like the hundredth time this month, I had one of those delightful experiences where something surprising pops out of your mouth, and you’re forced to listen warily to your own voice like a backseat driver, wondering if there’ll be enough room to turn around when the now-gravel road becomes dirt.

When I got to the point where I give an example of a fractal — electrons in an atom vs. planets in a solar system, or the veins in a leaf vs. the angles of the branches of the tree, etc. — my unconscious brain decided to take a detour to the Red Planet. But despite my initial horror (and maybe as a representation of poetic epiphany), I think this new example might work better than the others.  Or at least it’s only one picture to ask people to imagine.

Check out this false-color image of the Martian surface:


Those blue rocks in the basin aren’t really blue — that’s the false color.  But can you tell how big they are?  Are those blue rocks meters wide, half-buried in an ancient river bed, photographed by a satellite — or are they millimeters wide, scattered in the cracks of the desert floor, as seen by one of the Mars rovers a few feet away?

The caption doesn’t help: “The dried ocean bed of Meridiani Planum is the flattest plain in the solar system.  The mud of this ocean bed has dried into billions of mud polygons, some large enough to be seen from orbit.” Are those lighter objects some of the massive mud polygons or are they small pieces of one?

The only reason I know that this is a small-scale photo is because I know that I’m visiting the Mars rover website, and that I got to this image by looking at the Opportunity gallery.

That’s what fractals are.

Because the same patterns repeat across different levels of magnification, you can’t tell the scale of a fractal image just by looking.  What’s more, true fractals make scaling virtually irrelevant, because those same patters repeat over and over again into infinity (and into the infinitely small).  And so they make time and space virtually irrelevant — meaning only exists as a kind of ratio, a comparison of one portion to another.  In other words meaning only exists as metaphor.

That’s enough for now, but tomorrow I’m going to try to partially explain once and for all what makes American Fractal a fractal.


p.s. The only reason I was looking at Mars images in the first place is this article about potential fossils on Mars.  There are a lot of people who’ve been claiming to see fossils in the Spirit and Opportunity images for years, and it’s kind of like watching a horse race as mainstream science flirts with catching up.  Not being a geologist or a marine biologist, I have no idea what I’m looking at when I’m comparing vague shadows in the rocks to earthly sea shells.  But it’s damn cool to think about.

2 thoughts on “Fractilic Landscapes

  1. Tim, I do wish I could say that I’ve had a “Eureka!” moment, that the concept of fractals is now perfectly clear to me, but I haven’t, and it’s not. I’m pretty sure the fractal is not the blue rock itself. Is it the relationship between the blue rock and the surrounding landscape? If so, in what sense? Are we talking plane geometry? Solid? Something else entirely?

    If the relationship between the blue rock and the landscape, however we define it, is replicated on the surface of the blue rock (like the little girl on the Morton salt container), which I think I understood to be the case, then is the fractal that relationship? Is a fractal, then, not a thing at all?

    Obviously, I am thoroughly confused. The only positive thing I can say is that now, at least, I know that I don’t know.

  2. Pingback: The Post in Which I Explain Once and For All What Makes American Fractal a Fractal » Timothy Green

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