Background for PodCast BeadAlong
Almost 7 years ago I held a necklace of geometric stars made by Stacy Creamer, built to a design by Jean Power. Each star was made of five Warped Squares. I was entranced by the small miracle of the Warped Square; here, at last, was something that Didn’t Fit. I spend much of my life observing those telltale signs of complexity, things that Don’t Fit.
I now know these mysteries as Hypars
, or little hyperbolic planes. They are everything. They can even be Deconstructed, like in these earrings by Kim Van Antwerp. This is like.. intersecting hyperbolic planes. They might lead to shocking thoughts if worn near the brain.
Once I got going making my own geometric pieces, I became fixated on why the sturdy, reliable Flat Peyote Triangle seemed so much like the elusive Warped Square. Why herringbone increases looked exactly like decreases, even though they went on completely differently. I was so distracted by these questions that I found it difficult to comprehend the forms. My Triangles were oddly full of errors.
People asked me for most of last year why I wasn’t putting out a pattern book. Why was I, an artist and writer, instead inside the Skunk Works, or at MIT, or chasing around after topologists, asking about Clifford algebra, talking about quantum propulsion. WTF.
It wasn’t really that odd. I wanted to understand
before I published this time. I mean really understand. And I was beginning to realize the history of some of the forms I was seeing, and their implications.
The Kaleidocycle, for example, was neither an invention of beaders nor of origami artists. It is a classical arrangement of Mirror Tetrahedra (which answer to no man or woman) in a linkage. (Cycle above by Franklin Martin).
The linkage was described by Raoul Bricard
, a French mathematician, at the turn of the last century – along with many other machines and kinematic chains of nature that are still being studied. The cycle is an organic, essential machine that Nature knows well how to make, and you might see virus arranged in such a ring, or realize that social patterns resolve to the same kind of eternal rotation.
The crafting of Hypars into Star forms is also done by Nature. Origami artists make them, and computational origami studies the many arrangements they (and other hyperbolic, folded, pleated or energetic forms) can make. Erik and Marty Demaine name their arrangements of Hypars by how many “hats” they make put together
. Everyone has niche terminology for the forms of Nature, but none of us own them.
I think this is really worth contemplating when one hears people talking about how they discovered, created, or own a pattern, or arrangement of shapes. To use words like that, a person really has to do some digging. Beaders did NOT invent any of these shapes. But figuring out how to best make them in our materials is something, for sure. And I do feel we can contribute to their understanding. (Photo Erik Demaine with a folded paper Hypar, you can find the pattern here
The reason that I began in this field is that beading is one of the oldest things that humans do. And only humans do it. This fascinates me. The patterns, counts and shapes that we work with are elemental, universal, and they are bigger than mathematics, because they describe pure form.
Topology has been helpful, as has a more rigorous study of geometry. I can now see that the inside space of a Rick-Rack
or an All-Wing
is just a folded up polygon. A Six-Wing, in a flat representation, is like a dodecagon
, with half of its legs folded in. And in real life, maybe it’s like a dodecahedron, folded into 12 legs, 6 up and 6 down.
You know, during its construction, the 6-Point Rick-Rack makes each of these shapes:
So. When I try to understand how to make the thing: if the Rick-Rack is a folded up 12-gon, then what does the middle look like? A tinier version of the same. That’s where we should start, then, not with the outside line of the completely expanded form. Nature makes folded, spiky things all of the time. Look at this carrot seed!
Yes! It makes a carrot plant. Virus is spiky, too, and waves and frequencies represent as zigged lines. This is very elemental stuff. (Image by Rob Kesseler.
Nature has a kind of symmetry that cannot be denied.
So what I was hunting all of this time when I was looking for the smartest way to make a Zigged form was actually the middle of a Rick-Rack, the doughnut hole, as it were.
It turns out to be an even tinier spiked form; a tiny All-Wing. It looks like this, and it’s easy to see, and even easier to make.
And it’s our first Bead-A-Long.
Join us tomorrow to make your own tiny little All-Wing, the PodCast Bead.