The Fitful Flog

Yes, getting a little swirly in here. Curved surface folding adds a new axis to the fold: mountain/valley, left/right, up/down, curved/flat….I like it. Gritty, textural, doesn’t work 3 times out of 5. Oh, yeah.

This is a Coriolis Bowl, named for that swirling effect the Earth’s rotation adds to storms and whirlpools. Astute folders will note that this one has a counterclockwise rotation, suggesting that it was created somewhere in the Northern Hemisphere.

However, I urge our folding public to exercise caution. Coriolis storms have been known to move people out of (and into) Kansas. Which, we hear, is quite the cultural mecca these days, though we’re reserving judgment on this head — heard the same thing about Elk City, Oklahoma.

The crease pattern.

Update: Better crease pattern and some nice hints can be found here.

Say what? Well, we must call it something and that name may be unlovely, but it is not unapt.

It’s in two pieces, the top wrapping over the bottom. Or the other way around, doesn’t matter much.

If you’ve spent anytime at all with circles, you’ve noticed that it’s very easy to fold a hex grid. Circles were built for this. But where, you ask, do the curves come from? Easy — the edge. Circle’s only got the one. Look at the CP and note where the curves begin and end. Now, fold the edge over, so it connects the two points. See? Just bend the paper a little and start pinching in the curve. As you practice this, you’ll see how much more accurate your lines will become.

The Crease Pattern

This is the same as the Triskelion Dish, but with the corners folded under – I didn’t quite like the white showing. A trifle more complicated, but logical and more aesthetically satisfying. Like a nice bowl of Spicy Beef Soup.

We offer two files here, one the crease pattern: Sam-Taeguk Dish Crease Pattern

And the other a colored printout that suggests the Korean national symbol: Sam-Taeguk Dish in Color

And we say howdy to our readers in Korea.

I think I mentioned at some point that it was easy to make an elegant pentagon from a circle of paper. It is, but still, it’s not intuitive. Making polygons from circles has a lot in common with compass-and-straightedge work. Except paper is easier to work with and the straightedge can be marked up like crazy.

Pentagon from a Circle Sequenced Crease Pattern

Based on a method described by H.W. Richards in 1893 – not that I’ve seen this. I read about it at MathWorld.

Where Are The Phreakin’ Diagrams?

None, yet – and when there are, they’ll be debuting on a different stage. (We’ll link to it.)

Till then, an unimproved CP for the impatient: O3 Rose, 0.4

Or: O3 Rose Crease Pattern, Somewhat Improved.

Triskelion Dish

Now, I must go do some laundry.

georigami was asking about a CP for this model. There isn’t one yet, but he also notes I’ve been sketching on the paper. It’s not done, conceptually or artistically, but that’s no reason why you shouldn’t play along at home. If you fold the edges to the lines, you’ll see where the mountain folds want to go. If you get anything good, post it and ping me back.

Square Curves

This model came from a few different thoughts, one being Mélisande*‘s hints that my folds were becoming harder to figure out. Another was a comment of georigami‘s about tension and curves in paper.

I’m fond of this model because it has nice lines and is simple to make. It’s also a good introduction to curved folding. If it’s not evident from the crease pattern, the way you get the curves is to fold one edge to the middle and use it as a guide to pinch in a mountain fold. With practice, this will become increasingly easy and you can achieve a surprising amount of accuracy after a while. Even on a bumpy bus. The curves on the piece, both the downward swooping ones in the middle and the gentle ones on the sides, lend the model unexpected rigidity.

And it really remind me of the wildflower, trillium. Not just the curved pieces in the middle – the lobes of the bowl look not unlike its broad leaves.

I recommend a stout paper.

I was going to wait a bit before posting this, wait for understanding. But you know, I am so slow of apperception that for all of me, we might be up to our giblets in simultaneous Asian land wars before I decide I know what’s going on with this model.

Oh, that’s right.

So, why wait? I had thought I could talk about the curved folds in this piece with some sort of smooth Euclidean patter, but the arcs on this piece are not circle fragments, as I had thought, but some sort of hypebole. No, I’m not exaggerating, they really are hyperbolic. I just don’t know what to say about that.

So, give this a whack. It’s pretty. You like pretty, right? And the lovely Marcy says, if you put a loop of string through a piece of cardboard and collapsed the model around it, it could hang on the Christmas tree and be a nice gift box.

The crease pattern.

The City Fathers (a few Mothers, too) and the Department of Public Works have given me several broad hints lately that the art I pursue is no art at all, but a mere “craft or decorative art.” So be it.

Urania, Muse of Astronomy and Mathematics, who used to come see me now and again, has given me up for a rank poseur. Instead, I get visited by Cleanso, the Mt. Hellicon charwoman and part time Muse of Helpful Household Hints, and although everything she says is true, I am less inspired than I could wish to be.

“Red wine stains?” says my thick-armed vision, “Club soda will get that out.” or “Stubborn collar grime? Have you ever tried washing your freaking neck?”

Truth sucks.

I respond by posting a piece I promised to post over year ago. This is the 16 Sided Compass Rose Jar and a fine piece of work it is, indeed. And the City’s cruel barbs have forced me to admit, there’s not enough emotional content in my work. Cold dotted and dashed lines on an endless plane, hopelessly Apollonian stuff. This crease pattern bears the rebus of my dreamtime, because dreams are the fruit machine of the gods. Drop your dime, pull the lever and away you go. Happy dreams of love and royalty checks, sad dreams of old girlfriends and smelly sneakers.

It’s hard to decipher. The peppermill could be about my ambivalence on the loss of heavy industry in New England. Or maybe it was that I put too much pepper on my soup at lunch yesterday and liked it, anyway. The basilisk could express my trepidation that I am getting too stiff and slowly turning to stone. Or it might be some weird-ass religious symbol – they call them Jesu Christo lizards in South America, because they walk on water when startled. (In Venezuela, they walk on brown crude -Caracas Gold, Paramaribo Tea – same deal.) Point is, dreams are just things in juxtaposition to other things and sometimes, a pickle is just a gherkin. Judging by the symbols here, it looks like a happy dream, mainly.

Okay, brass tacks: it takes about an hour to do the precreasing. You’ve really got to want to do this. The construction method is largely the same as the 8 Sided Compass Rose Jar. Precrease; twist the central helix; swap the layers; collapse the edges. Here’s the crease pattern. Note that the second page tells you why the lines are where they are.

Elegant, you ask? No. The 2, 3 and 5 here started out as wild guesses and ended up as excellent approximations of the tangents they represent. Hey, this is art! Did you not see the emotional content above?