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?


origami madness said...

Fascinating! This is the kind of post that drew me to your blog in the first place. Minimalism has always intrigued me, so I love to see posts about it. I have two more rather wordy comments, just my musings about some of what you said:

You mention that flowers are an invention of insects, and imply that perhaps we share a fascination with flowers because of that. While this is certainly an interesting thought, I think we might have become associated with flowers more recently; humans were originally hunter-gatherers, and flowers were not only edible themselves in most cases (or some other part of the plant was edible, or they marked a spot where there would be fruit later on, etc,), but also symbolically connected to the fruit they would become, which explains the social reaction.

Also, about minimalism: another reason for minimalism to show up in origami is the strong influence of simplicity from Zen Buddhism, which has been well-established in Japanese culture for centuries. One-fold origami in this sense can be compared with some of the japanese/chinese calligraphy, where artists would often spend days trying to figure out how to draw a scene with the least number of strokes.


peterself said...


interesting thought, flowers are "insect-oriented" objects (yet we shouldn't forget a good number of birds); so, basically for insects flowers are related to feeding, in which case a human-equivalent for a flower should be a double king size cozy bed with a feast of food in the middle.

Maybe a key to identify what's minimum is to reproduce the basic feelings and emotions that an object (or a situation) triggers. I can adventure that flowers amaze humans by the contrast with their environment, most of the times due to the colors, but also their shapes and fragility (is interesting also this presence of fragility in the sexual relationship between plants, I can't avoid thinking on humans).

Sometimes we don't understand the meaning and objectives of a flower and we feel as "gifted" by nature, claiming the right to rip them from the plant, to put them on a vase to dry and dye, though they can help our loneliness for a while...

many regards (from a new reader).

lira lire lyra... said...

I don't know if you remember my. We knew ourselves the last year in Medellin Colombia. I mean to him that I like very much your flowers!!!
Andrea Acosta

saadya said...

Andrew, as you’ll see, I mostly don’t go along with ‘It all started in the hunter-gatherer phase’ types of explanations: the natural principles of attractiveness or of strikingness seem to have roots that go way, way back & encompass vast numbers of species—not just humans.

I give the hunter-gatherers this much: they were the first to invent CLOTHING, i.e. skins, and later fabrics. So there might be a connection with flowers here, they both being patterned, colorful membranes that have sex-appeal….

Fruit it seems to me do a good enough job of promoting themselves, without the need of flowers; what’s more the large numbers of flowers humans are drawn to don’t seem to be closely associated with ANY promise of future fruit.... In any case not all edible things (leaves, bark, tubers, raw meat) look pretty to us in the same organized way that flowers do. The surprise is that the floral advertisement is aimed at a VERY different niche-market than our own---but it still works for us.

Minimalism in origami is a vast subject, isn’t it? It may be that there are even new types of minimalism that origami was born specially to explore…. We’ll have to look into this

saadya said...

Thanks peterself, --I wasn’t forgetting the birds, I only wanted to focus on insects for dramatic effect. Birds are known to have better acuity and color vision than we do, and they’re much closer to us in the evolutionary tree, so it might seem SLIGHTLY less weird than it is with insects that things produced by bird aesthetics (whether by their choices of mates or their choices of flowers) draw OUR attention in something like the way it draws theirs.

It looks like I’m going to have to write, some day soon, that long disquisition on the broad convergences in animal aesthetics.... In a nutshell, my idea is that just as there is a great convergence in what are called “warning signals” and “warning coloration” in the animal world, there is also a convergence -- less focused, but still strong -- in what might be called “attracting signals”: those meant to call in a viewer for some interaction: mating, play, eating your fruit, gathering the young to you, getting parental attention, and so forth. These have elements in common with each other and also seem to follow similar principles across LOTS of different species. (It is a glaring oversight in my opinion that there is not even a name now in biology for this category to parallel “warning signals”). In any case, ‘attracting signals’ are like warnings in some respects—they have the be seen from afar and to get stronger as you come near-—but they also are defined in opposition to warning signals, so as not to be confused with them. So, for instance, if “aposematism” (warning colors) involves having two, large colors in wide, distinct pools or bands, and the colors are black + red/orange/yellow/white, an attracting color scheme will have instead 3 or 4 colors, or different ones than the above, or colors that blend in to each other softly rather than with a harsh boundary. And so forth----this can be taken pretty far.

A problem with bird coloration, now that I think of it, is that while it is driven mainly by sexual selection, sexual selection itself has two components: attracting females, and warning away competing males (or gaining social status etc). So that the striking traits you see on birds might be combinations of attracting + warning signals--making the above idea harder to tease out. (The same problem exists with other animals, especially since the showy ones are usually males) That’s why I liked what you wrote about flowers: flowers are a purer case, the aim is only to draw the pollinator in, almost never to threaten. And a flower does that, in part, by this wonderful fragility. Something of that same giftlike disarming fragility—surely it is that?—is what origami has borrowed for itself…

saadya said...

Hi Andrea, yes I do remember! I had a great time in Columbia.

J said...

Just wondering if you could explain how you went about adapting the minimal flower to a pop-up card...
I've been playing around trying to figure it out, and thought maybe I should ask.

Thanks a lot :)

saadya said...

Hi Janet

The sides of the closed flower get glued to the surfaces that open in the pop-up card. In the simplest card, which is just a book fold, you basically have to glue the flower near the spine. But you can make fancier (but still simple) surfaces that open and rise in the background card--and also multiply the spines available for gluing--by playing around with simple reverse-folds.

I hope all this isn't too obscure! Study the various images in recent & subsequent posts. Nothing is hidden!


Anonymous said...

Hi, just wondering if it was possible to get instructions for the flower card? Thanks!

Anonymous said...

Is it possible to get instructions for the flower card? Thanks!

Anonymous said...

i want the diagram please!!!