Monday, May 07, 2007

The Minimal Flower

We haven’t had a ‘natural history’ post on this Blog for a while, despite its name which I’m still committed to. But this investigation of flowers is triggering various new thoughts on flowers themselves, not just the origami of them; and its time to put these down---while they’re fresh and crude, in fact. Before a guarded professionalism, the curse of the times, withers their innocent bloom.

First, though, an old thought. No one seems specially surprised that flowers are delightful, exquisite, turn-ons, ideal objects for gifts, distinct and different and inviting of fine discriminations between them, a joy to multiple sense-organs, and connected more than etymologically with much of what we mean today by being “cultured” or “cultivated.”

The question is, why should any of this be. Flowers are basically an invention of insects, who taught the first angiosperms, 125 million years ago, what forms tickle their fancy. Why should what appeals to creepy-crawlers have anything to do with us? It’s been some time since we parted company. The last common ancestor between invertebrates and vertebrates lived 600 million years ago: a marsh-edge feeder, I understand, who had rudimentary vision at best. That there should be anything in common between us today as regards aesthetic tastes would seem a very considerable feat even for the sometimes astonishing forces of convergent evolution.

I have, needless to say, my own thoughts on what drives these confluences that turn up in nature’s aesthetics—which, presumably, I’ll get around to publishing one of these years, maybe after the war. (Hint: these theories are NOT chemical.) For now, though, it seems to me we ought to just be amazed.

Tinkering, lately, with those origami flowers, especially those irregular Miuras, I’ve noticed this: if you make tiny variations in the pattern of zigzags on two flowers that are otherwise identical (in color, size etc), you can’t include them both in the same ‘bouquet’ and expect them to be read as the same species of flower. The eye immediately picks out minute differences in angles, numbers of folds, and so on. Of course, in nature each individual flower unfurls, blooms, shakes in the wind, withers and goes through countless other changes while still leaving enough constants to allow a quick identification of it. Given a flower’s function—to get you from flower A to flower B of the same species on another plant, while bearing pollen—this is not altogether surprising.

But there’s been much talk in recent decades among psychologists, or nowadays, neurologists, about a ‘special face module’ in the brain that lets us quickly read human & animal faces, both for purposes of identification and to read the emotions expressed. That’s one reason, by the way, why it’s trivially easy to make SOMETHING in origami that will look like a human face (the module has a low activation threshold), but not at all easy to make the specific human face that you set out to, expressing a particular emotion, and have it be realistic rather than a caricature (there is high discrimination sensitivity). Now, I would bet that there is some similar module in our brain—maybe the same one—working for flowers too. And this would be another point of contact between ourselves and the insects. (You neuro grad students out there itching for a cute research project---here it is. Plug in those electrodes, see what lights up.)

[>Added February 2010: For a new scientific appreciation of the opposite idea, that insects (bees) have a 'face-recognition module' just as we do, see here. The researchers have not yet speculated on whether the module for recognizing faces is the same as the one for recognizing flowers.]

A question that’s as much about flowers as about the origami of them is: what are the minimum requirements for a thing to look like a flower?

At first glance it seems that almost anything can serve: a splash of color against the green is almost enough. The other day at the Beersheva Library's gallery I saw some splendid abstract, Pollock-like still-lifes by a Russian painter named “Zukhov”, who does just that: some random drips and daubs and splashes--and you have a vibrant bouquet. And in nature too, there are so fantastically many forms of flowers and whorls, the flora seeming to compete amongst themselves to come up with the latest fashions—that it would appear ludicrous to lay down any general rules for when a thing starts to look floral.

But this is origami, and we can't just leave it at that; we actually have to make something. And anyway for me, given the line I’ve been pursuing lately the question arose in a slightly different form. It bears repeating: What is the simplest origami pop-up shape you can make that can reasonably be called ‘a flower’?

This is, of course, an instance of a question asked when approaching any origami design. What is the simplest representation of an X that you can get away with? Or: what is the threshold where a bent-up sheet of paper with a few flaps, creases and bulges, turns into ‘an X’? Or: What will make fellow-designers green with envy at the thought: now why didn’t I come up with that?

Minimalism, I hasten to add, isn’t the only or even the main objective in design, just one possible goal; and it’s of course true that excesses in minimalism can be infuriating--seem to be insults to the viewer's attention or intelligence. (Most ‘one-crease’ origami strikes me that way.) Nevertheless, the minimalist effort does establish a sort of lower representational boundary that I maintain it is always important to find.

One of the simplest forms I can think of that counts as a pop-up, is the venerable and ubiquitous preliminary fold. Pull at the two flat exposed corners, and the two bent corners pop right out; push at those same points: the others climb right back in.

Unfortunately—but interestingly—this shape is not quite complex enough to be read as a flower. Even if you make it from a nice brightly colored square, say red or yellow, and prop it against some greenery. (Try it and see.) It is however enough for representing a simple roundish leaf, if the paper is green.

Here is small variation that makes the preliminary fold more compact, and so perhaps better for pop-up purposes. (Make all interior angles 60 degrees.) But the result will still be read as no more than a ‘leaf’--if even that. 'Design minimalism' may have been achieved, but 'representational minimalism' has not.

With a just trace of added complexity, however, the “preliminary fold” can be made to be read as a flower. Instead of dividing the surface into four, divide it into nine. It will still close back, more or less reliably. There are three main options for how the thing can close, but it doesn’t matter which one does so long as it closes.

Take off slight triangular amounts too from the north and south corners. The bent-back corners help close & open the model a little better in the middle. But they also let you read the slender mess of lines at the flower’s center-region as some visual noise within the geometric pattern: i.e., as the sex organs.

So it seems that what you need from a 'flower', besides a splash of color, is this: a minimal hint of geometric texture—i.e., a pattern. Division into four does not quite constitute a pattern, apparently; and patterns based on odd-numbers seem a touch more ‘organic’ than even ones. Further, a certain amount of noise, darkness or other difference should exist in the center of the form, to invite visual-tactile exploration: if you’re an insect who’s alighted, that’s where you’re going to be pulled to. Finally, I’ve found that the color of the flower really wants a green underline or undercup as contrast.

But that’s about IT. Further elaboration is of course welcome; but these seem to be the necessary minima.

--Is this an observation about flowers, or only about (origami) representations of them? Given that a flower works by putting on a show for us of insect-minds----is there a whole lot of difference?